Questa pagina contiene una tavola di integrali indefiniti di funzioni d'arco. Per altri integrali vedi Integrale § Tavole di integrali.
In questa pagina si assume che c denoti una costante diversa da 0.
![{\displaystyle \int \arcsin {\frac {x}{c}}\,dx=x\arcsin {\frac {x}{c}}+{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/444a6e76e395d1cab921a8de6414a45faa84a87d)
![{\displaystyle \int x\arcsin {\frac {x}{c}}\,dx=\left({\frac {x^{2}}{2}}-{\frac {c^{2}}{4}}\right)\arcsin {\frac {x}{c}}+{\frac {x}{4}}{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/250cee8385a63ca27b501383fadef3fdd3fb48d1)
![{\displaystyle \int x^{2}\arcsin {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arcsin {\frac {x}{c}}+{\frac {x^{2}+2c^{2}}{9}}{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3be1b55b77e7f7eb0d94b8ac5011e6202b4dbd0)
![{\displaystyle \int \arccos {\frac {x}{c}}\,dx=x\arccos {\frac {x}{c}}-{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7977aa9b1693b1d8f9a1372e191b66d09ed769)
![{\displaystyle \int x\arccos {\frac {x}{c}}\,dx=\left({\frac {x^{2}}{2}}-{\frac {c^{2}}{4}}\right)\arccos {\frac {x}{c}}-{\frac {x}{4}}{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8ad6cf248d5b3520849f4d17e09d7aba60763b1)
![{\displaystyle \int x^{2}\arccos {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arccos {\frac {x}{c}}-{\frac {x^{2}+2c^{2}}{9}}{\sqrt {c^{2}-x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb12d30457a97c184b290f9e7ddbd94ba660dc6)
![{\displaystyle \int \arctan {\frac {x}{c}}\,dx=x\arctan {\frac {x}{c}}-{\frac {c}{2}}\ln(c^{2}+x^{2})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d23ae118aa827d52dab59ba510e048f705c7f5f9)
![{\displaystyle \int x\arctan {\frac {x}{c}}\,dx={\frac {c^{2}+x^{2}}{2}}\arctan {\frac {x}{c}}-{\frac {cx}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61afc01a36c5b603bbef1301368c62df3ff4e23a)
![{\displaystyle \int x^{2}\arctan {\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\arctan {\frac {x}{c}}-{\frac {cx^{2}}{6}}+{\frac {c^{3}}{6}}\ln {c^{2}+x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c349b132590c4cca6782e374db9448726a377af8)
![{\displaystyle \int x^{n}\arctan {\frac {x}{c}}\,dx={\frac {x^{n+1}}{n+1}}\arctan {\frac {x}{c}}-{\frac {c}{n+1}}\int {\frac {x^{n+1}dx}{c^{2}+x^{2}}}\qquad {\mbox{(per }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/031097e0ebafe5135fed1bbbb8169912c0e074c2)
![{\displaystyle \int \operatorname {arcsec} {\frac {x}{c}}\,dx=x\operatorname {arcsec} {\frac {x}{c}}+{\frac {x}{c|x|}}\ln {|x\pm {\sqrt {x^{2}-1}}|}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d3602957fd66d74f4831735ba8b4802d833959)
![{\displaystyle \int \mathrm {arccot} \,{\frac {x}{c}}\,dx=x\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {c}{2}}\ln(c^{2}+x^{2})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c1acce8fa360e84fdeff795a57f656b7b56c098)
![{\displaystyle \int x\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {c^{2}+x^{2}}{2}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {cx}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/097c6976532d1d02e9498bb02962390fab37e3bd)
![{\displaystyle \int x^{2}\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {x^{3}}{3}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {cx^{2}}{6}}-{\frac {c^{3}}{6}}\ln(c^{2}+x^{2})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0700b31e5a7079deb4b87b956e5e31a3264ee3)
![{\displaystyle \int x^{n}\,\mathrm {arccot} \,{\frac {x}{c}}\,dx={\frac {x^{n+1}}{n+1}}\,\mathrm {arccot} \,{\frac {x}{c}}+{\frac {c}{n+1}}\int {\frac {x^{n+1}dx}{c^{2}+x^{2}}}\qquad {\mbox{(per }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1e4506ea8e90b12a5291503cf5a2bb1cb60e675)
- Murray R. Spiegel, Manuale di matematica, Etas Libri, 1974, pp. 82-84.