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list of integrals of inverse trigonometric functions wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 arcsine function integration formulas 2 arccosine function integration formulas 3 arctangent function integration formulas 4 arccotangent function integration formulas 5 arcsecant function integration formulas 6 arccosecant function integration formulas 7 see also 8 references toggle the table of contents list of integrals of inverse trigonometric functions 32 languages العربية bosanski català کوردی čeština чӑвашла ελληνικά español euskara فارسی français galego hrvatski հայերեն bahasa indonesia italiano 日本語 ភាសាខ្មែរ 한국어 македонски nederlands norsk bokmål русский srpskohrvatski српскохрватски slovenščina shqip српски srpski தமிழ் türkçe українська tiếng việt 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia this article does not cite any sources please help improve this article by adding citations to reliable sources unsourced material may be challenged and removed find sources list of integrals of inverse trigonometric functions news newspapers books scholar jstor june 2026 learn how and when to remove this message trigonometry outline history usage functions sin cos tan inverse generalized trigonometry reference identities exact constants tables unit circle laws and theorems sines cosines pythagorean theorem tangents cotangents calculus trigonometric substitution integrals inverse functions derivatives trigonometric series mathematicians hipparchus ptolemy brahmagupta al hasib al battani regiomontanus viète de moivre euler fourier v t e the following is a list of indefinite integrals antiderivatives of expressions involving the inverse trigonometric functions for a complete list of integral formulas see lists of integrals the inverse trigonometric functions are also known as the arc functions c is used for the arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known thus each function has an infinite number of antiderivatives there are three common notations for inverse trigonometric functions the arcsine function for instance could be written as sin 1 asin or as is used on this page arcsin for each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions arcsine function integration formulas edit arcsin x d x x arcsin x 1 x 2 c displaystyle int arcsin x dx x arcsin x sqrt 1 x 2 c arcsin a x d x x arcsin a x 1 a 2 x 2 a c displaystyle int arcsin ax dx x arcsin ax frac sqrt 1 a 2 x 2 a c x arcsin a x d x x 2 arcsin a x 2 arcsin a x 4 a 2 x 1 a 2 x 2 4 a c displaystyle int x arcsin ax dx frac x 2 arcsin ax 2 frac arcsin ax 4 a 2 frac x sqrt 1 a 2 x 2 4 a c x 2 arcsin a x d x x 3 arcsin a x 3 a 2 x 2 2 1 a 2 x 2 9 a 3 c displaystyle int x 2 arcsin ax dx frac x 3 arcsin ax 3 frac left a 2 x 2 2 right sqrt 1 a 2 x 2 9 a 3 c x m arcsin a x d x x m 1 arcsin a x m 1 a m 1 x m 1 1 a 2 x 2 d x m 1 displaystyle int x m arcsin ax dx frac x m 1 arcsin ax m 1 frac a m 1 int frac x m 1 sqrt 1 a 2 x 2 dx quad m neq 1 arcsin a x 2 d x 2 x x arcsin a x 2 2 1 a 2 x 2 arcsin a x a c displaystyle int arcsin ax 2 dx 2x x arcsin ax 2 frac 2 sqrt 1 a 2 x 2 arcsin ax a c arcsin a x n d x x arcsin a x n n 1 a 2 x 2 arcsin a x n 1 a n n 1 arcsin a x n 2 d x displaystyle int arcsin ax n dx x arcsin ax n frac n sqrt 1 a 2 x 2 arcsin ax n 1 a n n 1 int arcsin ax n 2 dx arcsin a x n d x x arcsin a x n 2 n 1 n 2 1 a 2 x 2 arcsin a x n 1 a n 1 1 n 1 n 2 arcsin a x n 2 d x n 1 2 displaystyle int arcsin ax n dx frac x arcsin ax n 2 n 1 n 2 frac sqrt 1 a 2 x 2 arcsin ax n 1 a n 1 frac 1 n 1 n 2 int arcsin ax n 2 dx quad n neq 1 2 arccosine function integration formulas edit arccos x d x x arccos x 1 x 2 c displaystyle int arccos x dx x arccos x sqrt 1 x 2 c arccos a x d x x arccos a x 1 a 2 x 2 a c displaystyle int arccos ax dx x arccos ax frac sqrt 1 a 2 x 2 a c x arccos a x d x x 2 arccos a x 2 arccos a x 4 a 2 x 1 a 2 x 2 4 a c displaystyle int x arccos ax dx frac x 2 arccos ax 2 frac arccos ax 4 a 2 frac x sqrt 1 a 2 x 2 4 a c x 2 arccos a x d x x 3 arccos a x 3 a 2 x 2 2 1 a 2 x 2 9 a 3 c displaystyle int x 2 arccos ax dx frac x 3 arccos ax 3 frac left a 2 x 2 2 right sqrt 1 a 2 x 2 9 a 3 c x m arccos a x d x x m 1 arccos a x m 1 a m 1 x m 1 1 a 2 x 2 d x m 1 displaystyle int x m arccos ax dx frac x m 1 arccos ax m 1 frac a m 1 int frac x m 1 sqrt 1 a 2 x 2 dx quad m neq 1 arccos a x 2 d x 2 x x arccos a x 2 2 1 a 2 x 2 arccos a x a c displaystyle int arccos ax 2 dx 2x x arccos ax 2 frac 2 sqrt 1 a 2 x 2 arccos ax a c arccos a x n d x x arccos a x n n 1 a 2 x 2 arccos a x n 1 a n n 1 arccos a x n 2 d x displaystyle int arccos ax n dx x arccos ax n frac n sqrt 1 a 2 x 2 arccos ax n 1 a n n 1 int arccos ax n 2 dx arccos a x n d x x arccos a x n 2 n 1 n 2 1 a 2 x 2 arccos a x n 1 a n 1 1 n 1 n 2 arccos a x n 2 d x n 1 2 displaystyle int arccos ax n dx frac x arccos ax n 2 n 1 n 2 frac sqrt 1 a 2 x 2 arccos ax n 1 a n 1 frac 1 n 1 n 2 int arccos ax n 2 dx quad n neq 1 2 arctangent function integration formulas edit arctan x d x x arctan x ln x 2 1 2 c displaystyle int arctan x dx x arctan x frac ln left x 2 1 right 2 c arctan a x d x x arctan a x ln a 2 x 2 1 2 a c displaystyle int arctan ax dx x arctan ax frac ln left a 2 x 2 1 right 2 a c x arctan a x d x x 2 arctan a x 2 arctan a x 2 a 2 x 2 a c displaystyle int x arctan ax dx frac x 2 arctan ax 2 frac arctan ax 2 a 2 frac x 2 a c x 2 arctan a x d x x 3 arctan a x 3 ln a 2 x 2 1 6 a 3 x 2 6 a c displaystyle int x 2 arctan ax dx frac x 3 arctan ax 3 frac ln left a 2 x 2 1 right 6 a 3 frac x 2 6 a c x m arctan a x d x x m 1 arctan a x m 1 a m 1 x m 1 a 2 x 2 1 d x m 1 displaystyle int x m arctan ax dx frac x m 1 arctan ax m 1 frac a m 1 int frac x m 1 a 2 x 2 1 dx quad m neq 1 arccotangent function integration formulas edit arccot x d x x arccot x ln x 2 1 2 c displaystyle int operatorname arccot x dx x operatorname arccot x frac ln left x 2 1 right 2 c arccot a x d x x arccot a x ln a 2 x 2 1 2 a c displaystyle int operatorname arccot ax dx x operatorname arccot ax frac ln left a 2 x 2 1 right 2 a c x arccot a x d x x 2 arccot a x 2 arccot a x 2 a 2 x 2 a c displaystyle int x operatorname arccot ax dx frac x 2 operatorname arccot ax 2 frac operatorname arccot ax 2 a 2 frac x 2 a c x 2 arccot a x d x x 3 arccot a x 3 ln a 2 x 2 1 6 a 3 x 2 6 a c displaystyle int x 2 operatorname arccot ax dx frac x 3 operatorname arccot ax 3 frac ln left a 2 x 2 1 right 6 a 3 frac x 2 6 a c x m arccot a x d x x m 1 arccot a x m 1 a m 1 x m 1 a 2 x 2 1 d x m 1 displaystyle int x m operatorname arccot ax dx frac x m 1 operatorname arccot ax m 1 frac a m 1 int frac x m 1 a 2 x 2 1 dx quad m neq 1 arcsecant function integration formulas edit arcsec x d x x arcsec x ln x x 2 1 c x arcsec x arcosh x c displaystyle int operatorname arcsec x dx x operatorname arcsec x ln left left x right sqrt x 2 1 right c x operatorname arcsec x operatorname arcosh x c arcsec a x d x x arcsec a x 1 a arcosh a x c displaystyle int operatorname arcsec ax dx x operatorname arcsec ax frac 1 a operatorname arcosh ax c x arcsec a x d x x 2 arcsec a x 2 x 2 a 1 1 a 2 x 2 c displaystyle int x operatorname arcsec ax dx frac x 2 operatorname arcsec ax 2 frac x 2 a sqrt 1 frac 1 a 2 x 2 c x 2 arcsec a x d x x 3 arcsec a x 3 arcosh a x 6 a 3 x 2 6 a 1 1 a 2 x 2 c displaystyle int x 2 operatorname arcsec ax dx frac x 3 operatorname arcsec ax 3 frac operatorname arcosh ax 6 a 3 frac x 2 6 a sqrt 1 frac 1 a 2 x 2 c x m arcsec a x d x x m 1 arcsec a x m 1 1 a m 1 x m 1 1 1 a 2 x 2 d x m 1 displaystyle int x m operatorname arcsec ax dx frac x m 1 operatorname arcsec ax m 1 frac 1 a m 1 int frac x m 1 sqrt 1 frac 1 a 2 x 2 dx quad m neq 1 arccosecant function integration formulas edit arccsc x d x x arccsc x ln x x 2 1 c x arccsc x arcosh x c displaystyle int operatorname arccsc x dx x operatorname arccsc x ln left left x right sqrt x 2 1 right c x operatorname arccsc x operatorname arcosh x c arccsc a x d x x arccsc a x 1 a artanh 1 1 a 2 x 2 c displaystyle int operatorname arccsc ax dx x operatorname arccsc ax frac 1 a operatorname artanh sqrt 1 frac 1 a 2 x 2 c x arccsc a x d x x 2 arccsc a x 2 x 2 a 1 1 a 2 x 2 c displaystyle int x operatorname arccsc ax dx frac x 2 operatorname arccsc ax 2 frac x 2 a sqrt 1 frac 1 a 2 x 2 c x 2 arccsc a x d x x 3 arccsc a x 3 1 6 a 3 artanh 1 1 a 2 x 2 x 2 6 a 1 1 a 2 x 2 c displaystyle int x 2 operatorname arccsc ax dx frac x 3 operatorname arccsc ax 3 frac 1 6 a 3 operatorname artanh sqrt 1 frac 1 a 2 x 2 frac x 2 6 a sqrt 1 frac 1 a 2 x 2 c x m arccsc a x d x x m 1 arccsc a x m 1 1 a m 1 x m 1 1 1 a 2 x 2 d x m 1 displaystyle int x m operatorname arccsc ax dx frac x m 1 operatorname arccsc ax m 1 frac 1 a m 1 int frac x m 1 sqrt 1 frac 1 a 2 x 2 dx quad m neq 1 see also edit differentiation of trigonometric functions mathematical process of finding the derivative of a trigonometric function list of trigonometric identities lists of integrals references edit v t e lists of integrals rational functions irrational algebraic functions trigonometric functions inverse trigonometric functions hyperbolic functions inverse hyperbolic functions exponential functions logarithmic functions gaussian functions definite integrals retrieved from https en wikipedia org w index php title list_of_integrals_of_inverse_trigonometric_functions oldid 1359023543 category lists of integrals hidden categories articles with short description short description is different from wikidata articles lacking sources from june 2026 all articles lacking sources this page was last edited on 12 june 2026 at 15 17 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents list of integrals of inverse trigonometric functions 32 languages add topic