Contenu

A.3. Intégrales trigonométriques inverses

\int arcsin u d u = u arcsin u + 1 - u^{2} + C

\int arccos u d u = u arccos u - 1 - u^{2} + C

\int arctan u d u = u arctan u - \frac{1}{2} ln (1 + u^{2}) + C

u

\int u arcsin u d u = \frac{2 u ^{2} - 1}{4} arcsin u + \frac{u 1 - u ^{2}}{4} + C

\int u arctan u d u = \frac{u ^{2} + 1}{2} arctan u - \frac{u}{2} + C

n \neq = - 1

\int u^{n} arcsin u d u = \frac{1}{n + 1} [u^{n + 1} arcsin u - \int \frac{u ^{n + 1} d u}{1 - u ^{2}}]

\int u^{n} arccos u d u = \frac{1}{n + 1} [u^{n + 1} arccos u + \int \frac{u ^{n + 1} d u}{1 - u ^{2}}]

\int u^{n} arctan u d u = \frac{1}{n + 1} [u^{n + 1} arctan u - \int \frac{u ^{n + 1} d u}{1 + u ^{2}}]