Ondorengoa funtzio irrazionalen integralen zerrenda bat da (jatorrizkoak edo antideribatuak). Integralen zerrenda osatuago nahi baduzu, ikusi integralen zerrenda.
Bere barnean (x² +a²)-ren erroa daukaten funtzioen integralak
![{\displaystyle \int r\;dx={\frac {1}{2}}\left(xr+a^{2}\,\ln \left(x+r\right)\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fd519ba0542e57b54a978ba84694e506bfd9a26)
![{\displaystyle \int r^{3}\;dx={\frac {1}{4}}xr^{3}+{\frac {1}{8}}3a^{2}xr+{\frac {3}{8}}a^{4}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc97c30a4823de6412533ddbae1868dfaa8d821)
![{\displaystyle \int r^{5}\;dx={\frac {1}{6}}xr^{5}+{\frac {5}{24}}a^{2}xr^{3}+{\frac {5}{16}}a^{4}xr+{\frac {5}{16}}a^{6}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/45451079405fdd21a461cde63f54710cc9bf33c1)
![{\displaystyle \int xr\;dx={\frac {r^{3}}{3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/90d18a7f64cfdf847e57edb171da6e947572b86f)
![{\displaystyle \int xr^{3}\;dx={\frac {r^{5}}{5}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ceed53e12be0e579bc437b4814e528a98cd35e7)
![{\displaystyle \int xr^{2n+1}\;dx={\frac {r^{2n+3}}{2n+3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe57bd8718c850c5fc37914f5b02846e70a8b94)
![{\displaystyle \int x^{2}r\;dx={\frac {xr^{3}}{4}}-{\frac {a^{2}xr}{8}}-{\frac {a^{4}}{8}}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05d32439f07196a63d44d8e3ad881caba768c705)
![{\displaystyle \int x^{2}r^{3}\;dx={\frac {xr^{5}}{6}}-{\frac {a^{2}xr^{3}}{24}}-{\frac {a^{4}xr}{16}}-{\frac {a^{6}}{16}}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7238a08b2dd8448a87d01179d05b2218b51a5d7)
![{\displaystyle \int x^{3}r\;dx={\frac {r^{5}}{5}}-{\frac {a^{2}r^{3}}{3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97ae1b756da1ede2908c90fb890b1e769f97f5ea)
![{\displaystyle \int x^{3}r^{3}\;dx={\frac {r^{7}}{7}}-{\frac {a^{2}r^{5}}{5}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff413fde069a2b237196d24b86e888bc55ca2c35)
![{\displaystyle \int x^{3}r^{2n+1}\;dx={\frac {r^{2n+5}}{2n+5}}-{\frac {a^{3}r^{2n+3}}{2n+3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70b10624c30a0ee4872917961693d1eed24477ab)
![{\displaystyle \int x^{4}r\;dx={\frac {x^{3}r^{3}}{6}}-{\frac {a^{2}xr^{3}}{8}}+{\frac {a^{4}xr}{16}}+{\frac {a^{6}}{16}}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41c4d6c3e8a748f948ee37bc71256f566016e7f3)
![{\displaystyle \int x^{4}r^{3}\;dx={\frac {x^{3}r^{5}}{8}}-{\frac {a^{2}xr^{5}}{16}}+{\frac {a^{4}xr^{3}}{64}}+{\frac {3a^{6}xr}{128}}+{\frac {3a^{8}}{128}}\ln \left(x+r\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d335f3a7b7a165804ec770dbe077ef4130ebb029)
![{\displaystyle \int x^{5}r\;dx={\frac {r^{7}}{7}}-{\frac {2a^{2}r^{5}}{5}}+{\frac {a^{4}r^{3}}{3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02290516b5e0ba00d1740531556fc72f1ef259c8)
![{\displaystyle \int x^{5}r^{3}\;dx={\frac {r^{9}}{9}}-{\frac {2a^{2}r^{7}}{7}}+{\frac {a^{4}r^{5}}{5}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/31c0be16d31b5dd86c18f5d5334b09e34b7b7239)
![{\displaystyle \int x^{5}r^{2n+1}\;dx={\frac {r^{2n+7}}{2n+7}}-{\frac {2a^{2}r^{2n+5}}{2n+5}}+{\frac {a^{4}r^{2n+3}}{2n+3}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ba05ede443f4dad41efbe05666607d48f0f9d6a)
![{\displaystyle \int {\frac {r\;dx}{x}}=r-a\ln \left|{\frac {a+r}{x}}\right|=r-a\sinh ^{-1}{\frac {a}{x}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/935bf83d3b1c3ecf08737948eb1e383aa90f057d)
![{\displaystyle \int {\frac {r^{3}\;dx}{x}}={\frac {r^{3}}{3}}+a^{2}r-a^{3}\ln \left|{\frac {a+r}{x}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bfd09256a55f895ddc9ae622db285b55d3f414b)
![{\displaystyle \int {\frac {r^{5}\;dx}{x}}={\frac {r^{5}}{5}}+{\frac {a^{2}r^{3}}{3}}+a^{4}r-a^{5}\ln \left|{\frac {a+r}{x}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18ef4dbb6fee79dea45d99a4d0f676ee94d6bf75)
![{\displaystyle \int {\frac {r^{7}\;dx}{x}}={\frac {r^{7}}{7}}+{\frac {a^{2}r^{5}}{5}}+{\frac {a^{4}r^{3}}{3}}+a^{6}r-a^{7}\ln \left|{\frac {a+r}{x}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f02d71f9ae708dc01a2bdaa95b7261d6f406c8e)
![{\displaystyle \int {\frac {dx}{r}}=\sinh ^{-1}{\frac {x}{a}}=\ln \left|x+r\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4604d6d3a6daccf7d1828bfc8d20665bebf60ea7)
![{\displaystyle \int {\frac {dx}{r^{3}}}={\frac {x}{a^{2}r}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f91a0f52588b690b3a3bc597cbbad038366fa832)
![{\displaystyle \int {\frac {x\,dx}{r}}=r+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9416e166c5e4c55ee79c25a5b9d5ee977f975768)
![{\displaystyle \int {\frac {x\,dx}{r^{3}}}=-{\frac {1}{r}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a2a728f4e79c458c9ab647d262e87cbfcc2712)
![{\displaystyle \int {\frac {x^{2}\;dx}{r}}={\frac {x}{2}}r-{\frac {a^{2}}{2}}\,\sinh ^{-1}{\frac {x}{a}}={\frac {x}{2}}r-{\frac {a^{2}}{2}}\ln \left|x+r\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/806a590ea9342ba4db54582c056f0617a75856aa)
![{\displaystyle \int {\frac {dx}{xr}}=-{\frac {1}{a}}\,\sinh ^{-1}{\frac {a}{x}}=-{\frac {1}{a}}\ln \left|{\frac {a+r}{x}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7599d2b26eb1887f7e64fa0e92a44271fef7afb9)
Bere barnean (x² -a²)-ren erroa daukaten funtzioen integralak
Kasu honetan
izan behar da, bestela
bada, begiratu hurrengo atala.
![{\displaystyle \int xs\;dx={\frac {1}{3}}s^{3}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9522e66195ece4c08b9a76949c85070cfaea1)
![{\displaystyle \int {\frac {s\;dx}{x}}=s-a\cos ^{-1}\left|{\frac {a}{x}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8908590ca348b34bbbc1b5ae906ac5004c2bd13)
![{\displaystyle \int {\frac {dx}{s}}=\int {\frac {dx}{\sqrt {x^{2}-a^{2}}}}=\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/afb40309a8e882eeac674492837da5b3aac287e8)
Kontuan hartu behar dugu
dela, non
-ren balio positiboa hartzen den.
![{\displaystyle \int {\frac {x\;dx}{s}}=s+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67292a47864c1267d4f2134fc38c0a264534f33e)
![{\displaystyle \int {\frac {x\;dx}{s^{3}}}=-{\frac {1}{s}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf4be0a19862eaf530009ec904d3ca7d8a10f6fd)
![{\displaystyle \int {\frac {x\;dx}{s^{5}}}=-{\frac {1}{3s^{3}}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/524ab8acb2979c7ea515e98982f4442ff7a309e5)
![{\displaystyle \int {\frac {x\;dx}{s^{7}}}=-{\frac {1}{5s^{5}}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf8ab5c44369bba29ba0d399f83f6de24973b97b)
![{\displaystyle \int {\frac {x\;dx}{s^{2n+1}}}=-{\frac {1}{(2n-1)s^{2n-1}}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e616abb35cb27233866602da5355ff419b0865f)
![{\displaystyle \int {\frac {x^{2m}\;dx}{s^{2n+1}}}=-{\frac {1}{2n-1}}{\frac {x^{2m-1}}{s^{2n-1}}}+{\frac {2m-1}{2n-1}}\int {\frac {x^{2m-2}\;dx}{s^{2n-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/819c367c3f01849bfcfa4f310a2e2fc8d4630d2e)
![{\displaystyle \int {\frac {x^{2}\;dx}{s}}={\frac {xs}{2}}+{\frac {a^{2}}{2}}\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09508bbb2ad68f8877f049e3deff762b6c7540c1)
![{\displaystyle \int {\frac {x^{2}\;dx}{s^{3}}}=-{\frac {x}{s}}+\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd0762764654f90af44be9ea2af3d0615ca6a0ee)
![{\displaystyle \int {\frac {x^{4}\;dx}{s}}={\frac {x^{3}s}{4}}+{\frac {3}{8}}a^{2}xs+{\frac {3}{8}}a^{4}\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/143a9855eb38aef618fb8648752e7f71d67055a3)
![{\displaystyle \int {\frac {x^{4}\;dx}{s^{3}}}={\frac {xs}{2}}-{\frac {a^{2}x}{s}}+{\frac {3}{2}}a^{2}\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a3442d5b3e116b93f2faf1db347f100c510f7b7)
![{\displaystyle \int {\frac {x^{4}\;dx}{s^{5}}}=-{\frac {x}{s}}-{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}+\ln \left|{\frac {x+s}{a}}\right|+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/da7950a5ccbf048dd08063197ac9f3c21879d254)
![{\displaystyle \int {\frac {x^{2m}\;dx}{s^{2n+1}}}=(-1)^{n-m}{\frac {1}{a^{2(n-m)}}}\sum _{i=0}^{n-m-1}{\frac {1}{2(m+i)+1}}{n-m-1 \choose i}{\frac {x^{2(m+i)+1}}{s^{2(m+i)+1}}}+K\qquad {\mbox{(}}n>m\geq 0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ac4a8c37df5d281bec42703ebd8d805faa6aeb9)
![{\displaystyle \int {\frac {dx}{s^{3}}}=-{\frac {1}{a^{2}}}{\frac {x}{s}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95381d37c908e5fac193568db588e6140dd83033)
![{\displaystyle \int {\frac {dx}{s^{5}}}={\frac {1}{a^{4}}}\left[{\frac {x}{s}}-{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}\right]+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f9d9afa0d03a1462c66abec3875257421e5b477)
![{\displaystyle \int {\frac {dx}{s^{7}}}=-{\frac {1}{a^{6}}}\left[{\frac {x}{s}}-{\frac {2}{3}}{\frac {x^{3}}{s^{3}}}+{\frac {1}{5}}{\frac {x^{5}}{s^{5}}}\right]+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/401670d3de0e3db3a6a0de2e1b733b0631e8162e)
![{\displaystyle \int {\frac {dx}{s^{9}}}={\frac {1}{a^{8}}}\left[{\frac {x}{s}}-{\frac {3}{3}}{\frac {x^{3}}{s^{3}}}+{\frac {3}{5}}{\frac {x^{5}}{s^{5}}}-{\frac {1}{7}}{\frac {x^{7}}{s^{7}}}\right]+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/55164710854a9acae1ded849053b1e04442a039e)
![{\displaystyle \int {\frac {x^{2}\;dx}{s^{5}}}=-{\frac {1}{a^{2}}}{\frac {x^{3}}{3s^{3}}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f2a6a6db99c89326826ee4bb2856f60279440e2)
![{\displaystyle \int {\frac {x^{2}\;dx}{s^{7}}}={\frac {1}{a^{4}}}\left[{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}-{\frac {1}{5}}{\frac {x^{5}}{s^{5}}}\right]+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c124df10e4e6c2adc489b7e70252d2502c1374f3)
![{\displaystyle \int {\frac {x^{2}\;dx}{s^{9}}}=-{\frac {1}{a^{6}}}\left[{\frac {1}{3}}{\frac {x^{3}}{s^{3}}}-{\frac {2}{5}}{\frac {x^{5}}{s^{5}}}+{\frac {1}{7}}{\frac {x^{7}}{s^{7}}}\right]+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38338bbe093db76aa7c669f60dc995ecf37940a5)
Bere barnean (a²-x²)-ren erroa daukaten funtzioen integralak
![{\displaystyle \int u\;dx={\frac {1}{2}}\left(xu+a^{2}\arcsin {\frac {x}{a}}\right)+K\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fde7db66e9fc6c57a60dc92cb4a96996144d8aca)
![{\displaystyle \int xu\;dx=-{\frac {1}{3}}u^{3}+K\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de6fd74b90f72ce2c9cb738cd4a1316f3f8ab929)
![{\displaystyle \int {\frac {u\;dx}{x}}=u-a\ln \left|{\frac {a+u}{x}}\right|+K\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef99a72e73e1dfa90b795d04b15f72bab5aa0e95)
![{\displaystyle \int {\frac {dx}{u}}=\arcsin {\frac {x}{a}}+K\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/beea912afb1d4a8dcfa670af54ad0e6df6a6219c)
![{\displaystyle \int {\frac {x^{2}\;dx}{u}}={\frac {1}{2}}\left(-xu+a^{2}\arcsin {\frac {x}{a}}\right)+K\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ade46b2fb0aadcbdde774e0de8a9b25aaa7695f)
![{\displaystyle \int u\;dx={\frac {1}{2}}\left(xu-\operatorname {sgn} x\,\cosh ^{-1}\left|{\frac {x}{a}}\right|\right)+K\qquad {\mbox{( }}|x|\geq |a|{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2523859ace84ad43903f1abf69ebd92497ba356)
Bere barnean (ax²+bx+c)-ren erroa daukaten funtzioen integralak
![{\displaystyle \int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\ln \left|2{\sqrt {a}}R+2ax+b\right|+K\qquad {\mbox{( }}a>0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db75be22fa3fbcfe714cffd6af377b312b543a7c)
![{\displaystyle \int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\,\sinh ^{-1}{\frac {2ax+b}{\sqrt {4ac-b^{2}}}}+K\qquad {\mbox{( }}a>0{\mbox{, }}4ac-b^{2}>0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a495af94a0f879dff56c78902da7fe115d2e55d)
![{\displaystyle \int {\frac {dx}{R}}={\frac {1}{\sqrt {a}}}\ln |2ax+b|+K\quad {\mbox{( }}a>0{\mbox{, }}4ac-b^{2}=0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81c2de6a7f24d8f7018507e7c3c8801088d13d4d)
![{\displaystyle \int {\frac {dx}{R}}=-{\frac {1}{\sqrt {-a}}}\arcsin {\frac {2ax+b}{\sqrt {b^{2}-4ac}}}+K\qquad {\mbox{( }}a<0{\mbox{, }}4ac-b^{2}<0{\mbox{, }}\left|2ax+b\right|<{\sqrt {b^{2}-4ac}}{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91e44766dd64f7280a0411e64d07165cbc08966e)
![{\displaystyle \int {\frac {dx}{R^{3}}}={\frac {4ax+2b}{(4ac-b^{2})R}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2bf67c6859ad2612f53c5f13fbcd0313ea767b73)
![{\displaystyle \int {\frac {dx}{R^{5}}}={\frac {4ax+2b}{3(4ac-b^{2})R}}\left({\frac {1}{R^{2}}}+{\frac {8a}{4ac-b^{2}}}\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/349bf2316e591211f81ccd8cb1a8c332bfc9bef5)
![{\displaystyle \int {\frac {dx}{R^{2n+1}}}={\frac {2}{(2n-1)(4ac-b^{2})}}\left({\frac {2ax+b}{R^{2n-1}}}+4a(n-1)\int {\frac {dx}{R^{2n-1}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6fd19c82abfd6ab01d93cc3f2691059d4b4915c)
![{\displaystyle \int {\frac {x}{R}}\;dx={\frac {R}{a}}-{\frac {b}{2a}}\int {\frac {dx}{R}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6880a823009f7d8fe7e2579fa228324ef0d15f03)
![{\displaystyle \int {\frac {x}{R^{3}}}\;dx=-{\frac {2bx+4c}{(4ac-b^{2})R}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efa4baed99c7bf7ad179cece9c37115feaf0b7b4)
![{\displaystyle \int {\frac {x}{R^{2n+1}}}\;dx=-{\frac {1}{(2n-1)aR^{2n-1}}}-{\frac {b}{2a}}\int {\frac {dx}{R^{2n+1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de6de2ef912d111ee50377af9daaf84b45633498)
![{\displaystyle \int {\frac {dx}{xR}}=-{\frac {1}{\sqrt {c}}}\ln \left({\frac {2{\sqrt {c}}R+bx+2c}{x}}\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ad37c3640edba56bf9ab5d485e5b468c112b7fb)
![{\displaystyle \int {\frac {dx}{xR}}=-{\frac {1}{\sqrt {c}}}\sinh ^{-1}\left({\frac {bx+2c}{|x|{\sqrt {4ac-b^{2}}}}}\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a667c799597cfcd027b9f03145590555e343ed5c)
Bere barnean (ax+b)-ren erroa daukaten funtzioen integralak
![{\displaystyle \int {\frac {dx}{\sqrt {ax+b}}}\,=\,{\frac {2{\sqrt {ax+b}}}{a}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf606c433aa6710872ddfe8a0b6dda49e365d0c)
![{\displaystyle \int {\frac {dx}{x{\sqrt {ax+b}}}}\,=\,{\frac {-2}{\sqrt {b}}}\tanh ^{-1}{\sqrt {\frac {ax+b}{b}}}+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bcb899f8470ea734fcb461cd85bc5e589284b2ae)
![{\displaystyle \int {\frac {\sqrt {ax+b}}{x}}\,dx\;=\;2\left({\sqrt {ax+b}}-{\sqrt {b}}\tanh ^{-1}{\sqrt {\frac {ax+b}{b}}}\right)+K}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eede3521c11e6628edd9303b0d26289ca4fbb367)
![{\displaystyle \int {\frac {x^{n}}{\sqrt {ax+b}}}\,dx\;=\;{\frac {2}{a(2n+1)}}\left(x^{n}{\sqrt {ax+b}}-bn\int {\frac {x^{n-1}}{\sqrt {ax+b}}}\,dx\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc428e49a57674b857b5c7373aa652a042179e60)
![{\displaystyle \int x^{n}{\sqrt {ax+b}}\,dx\;=\;{\frac {2}{2n+1}}\left(x^{n+1}{\sqrt {ax+b}}+bx^{n}{\sqrt {ax+b}}-nb\int x^{n-1}{\sqrt {ax+b}}\,dx\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd8c3bf8206cec454702eaab4cc9d3bf911983b1)
Bibliografia
- Peirce, Benjamin Osgood. (1929). «3. atalaburua» A Short Table of Integrals. (3. argitaraldia) Boston: Ginn and Co, 16.–30 or..
- Milton Abramowitz & Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1972, Dover: New York. (Ikusi: capítol 3.)