calcul intégrale 2 bac science math Série 1

Calculer les intégrales suivantes:

1- $I={\int }_1^9(3x-2{)}^{-3/2}dx$

2- $I={\int }_0^{\ln 2}\frac{\sqrt{e^x}}{{(1+\sqrt{e^x})}^2}dx(t=\sqrt{e^x})$

3- $I={\int }_0^{\frac{\pi }{2}}\frac{cos(x)}{1+sin²(x)}dx(t=sin(x))$

4- $I={\int }_1^e{x}^4\ln xdx$

5- $I={\int }_1^2(x+\frac{1}{x})\ln xdx$

6- $I={\int }_{\sqrt{3}}^{2\sqrt{2}}\frac{2}{x\sqrt{1+x²}}dx$

7- $I={\int }_0^{\pi }\frac{\sin 2x}{\sqrt{1+3{\cos }^{2}x}}dx$

8- $I_1={\int }_0^{\ln 2}{(e^x-1)}^5{e}^{2x}dx$

9- $I={\int }_{-1}^4\frac{1}{x+\sqrt{x}}dx$

10- $I={\int }_1^e(1-\frac{1}{x²})\ln xdx$

11- $I={\int }_0^1\ln (x+\sqrt{x^2+1})dx$

12- $I={\int }_1^3\frac{\ln (x+1)}{x^2}dx$

13- $I={\int }_0^{\ln \sqrt{3}}\frac{1}{e^x(1+e^{2x})}dx(t=e^{-x})$

14- $I_1{=}_1{\int }_{\pi /4}^{0}tg(x{)}^{5}xdx$

15- $I={\int }_{\pi /4}^{\pi /3}(\frac{1}{\cos (x{)}^2}-4\cos (2x))dx$

16- $I={\int }_0^{\pi /4}\frac{tg(x{)}^{\frac{1}{3}}}{cos(x{)}^6}dx$

17- $I={\int }_1^{\sqrt{3}}\frac{1-x²}{(x²+1{)}^2}-ln(x)dx$

18- $I={\int }_0^4\sqrt{16-x^2}dx$

19- $I={\int }_{-\pi /2}^0\frac{1}{1-\sin (x)}dx$

20- $I={\int }_0^{\pi /2}{e}^x\cos (x)dx$

21- $I={\int }_0^1\frac{3x^2-4x+5}{x^2+1}dx$

22- $I={\int }_0^{\frac{\pi }{2}}\sin (x{)}^4\cos (x{)}^{5}dx$

23- $I={\int }_1^4\frac{4}{1+\sqrt{x}}dx$

24- $I={\int }_0^1\frac{e^x-e^{-x}}{e^x+e^{-x}}dx$

25- $I={\int }_0^1\frac{1}{2+e^{2x}}dx$

26- $I={\int }_0^1\ln \left(\frac{1}{1+x^2}\right)dx$

27- $I={\int }_{\frac{1}{e}}^{e²}\frac{|\ln x|}{x}dx$

28- $I={\int }_0^3\frac{x}{(x+1)\sqrt{x+1}}dx$

29- $I={\int }_1^{e^2}\frac{\ln (1+\sqrt{x})}{x+\sqrt{x}}dx$

30- $I={\int }_{\ln (\pi /4)}^{\ln (\pi /2)}{e}^{2x}\sin \left(e^x\right)dx(t=e^x)$

31- $I={\int }_1^e\frac{e^x(e^x+x+1)}{{(e^x+1)}^2}\ln xdx$

32- $I={\int }_{\ln (2)}^{2\ln (2)}\sqrt{e^x-1}dx$

33- $I={\int }_0^{\pi /4}\frac{x\sin x}{{\cos }^{5}x}dx$

34- $I={\int }_{\sqrt{3}}^{2\sqrt{2}}\frac{2}{x\sqrt{1+x^2}}dx$

35- $I={\int }_0^{\pi }\sqrt{1+\sin x}dx$