exo7 832

Calculer les primitives suivantes.

1

\(\displaystyle\int e^{\sin^2x} \sin2x\,dx\).

2

\(\displaystyle\int\cos^5t\,dt\) ; \(\displaystyle\int\cosh^3t\,dt\); \(\displaystyle\int\cos^4t\,dt\) ; \(\displaystyle\int\sinh^4t\,dt\).

3

\(\displaystyle\int x^3 e^x\,dx\).

4

\(\displaystyle\int\ln x \,dx\) ; \(\displaystyle\int x\ln x\,dx\); \(\displaystyle\int\arcsin x \,dx\).

5

\(\displaystyle\int\cosh t \sin t \, dt\).

6

\(\displaystyle\int{dx \over\sin x}\).

7

\(\displaystyle\int\sqrt{a^2-x^2}\,dx\).

8

\(\displaystyle\int{e^{2x}\over\sqrt{e^x+1}}\,dx\).

9

\(\displaystyle\int e^{ax}\cos bx \,dx\) ; \(\displaystyle\int e^{ax}\sin bx \,dx\).

10

\(\displaystyle\int\sqrt{x \over(1-x)^3}\,dx\)pour\(0<x<1\).

11

\(\displaystyle\int{x^2 \over\sqrt{1-x^2}}\,dx\).

12

\(\displaystyle\int{dx \over\cos x+2\sin x +3}\).

13

\(\displaystyle\int{\sqrt x\,dx \over\sqrt{a^3-x^3}}\) avec \(0<x<a\).

14

\(\displaystyle\int{\cosh x\over\cosh x+\sinh x}\,dx\).