Calculer les intégrales suivantes:
1- \(I=\int_{1}^{9}(3x-2)^{-3/2} \quad dx\)
2- \(I=\int_{0}^{\ln 2} \frac{\sqrt{e^{x}}}{\left(1+\sqrt{e^{x}}\right)^{2}} \quad dx \quad\left(t=\sqrt{e^{x}}\right)\)
3- \(I=\int_{0}^{\frac{π}{2}}\frac{cos(x)}{1+sin²(x)}\quad dx \quad\left(t=sin(x)\right)\)
4- \(I=\int_{1}^{e} x^{4} \ln x \quad dx\)
5- \(I=\int_{1}^{2}\left(x+\frac{1}{x}\right) \ln x \quad dx\)
6- \(I=\int_{\sqrt{3}}^{2\sqrt{2}}\frac{2}{x\sqrt{1+x²}} \quad dx\)
7- \(I=\int_{0}^{\pi} \frac{\sin 2 x}{\sqrt{1+3 \cos ^{2} x}} \quad dx\)
8- \(I_{1}=\int_{0}^{\ln 2}\left(e^{x}-1\right)^{5} e^{2x} \quad dx\)
9- \(I=\int_{-1}^{4} \frac{1}{x+\sqrt{x}} \quad dx\)
10- \(I=\int_{1}^{e} (1-\frac{1}{x²}) \ln x \quad dx\)
11- \(I=\int_{0}^{1} \ln \left(x+\sqrt{x^{2}+1}\right) \quad dx\)
12- \(I=\int_{1}^{3} \frac{\ln (x+1)}{x^{2}} \quad dx\)
13- \(I=\int_{0}^{\ln \sqrt{3}} \frac{1}{e^{x}\left(1+e^{2 x}\right)} \quad dx\quad(t=e^{-x})\)
14- \(I_{1}=_{1} \int_{\pi/4}^{0} tg(x) ^{5} x \quad dx\)
15- \(I=\int_{\pi / 4}^{\pi / 3}\left(\frac{1}{\cos(x) ^{2} }-4 \cos(2x)\right) \quad dx\)
16- \(I=\int_{0}^{\pi / 4} \frac{tg(x)^{\frac{1}{3}}}{cos(x)^{6}} \quad dx\)
17- \(I=\int_{1}^{\sqrt{3}} \frac{1-x²}{(x²+1)^{2}}-ln(x) \quad dx\)
18- \(I=\int_{0}^{4} \sqrt{16-x^{2}} \quad dx\)
19- \(I=\int_{-\pi / 2}^{0} \frac{1}{1-\sin(x)} \quad dx\)
20- \(I=\int_{0}^{\pi /2} e^{x}\cos(x) \quad dx\)
21- \(I=\int_{0}^{1} \frac{3 x^{2}-4 x+5}{x^{2}+1} \quad dx\)
22- \(I=\int_{0}^{\frac{\pi}{2}} \sin(x) ^{4} \cos(x)^{5} \quad dx\)
23- \(I=\int_{1}^{4} \frac{4}{1+\sqrt{x}} \quad dx\)
24- \(I=\int_{0}^{1} \frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \quad dx\)
25- \(I=\int_{0}^{1} \frac{1}{2+e^{2x}} \quad dx\)
26- \(I=\int_{0}^{1} \ln \left(\frac{1}{1+x^{2}}\right) \quad dx\)
27- \(I=\int_{\frac{1}{e}}^{e²} \frac{|\ln x|}{x}\quad dx\)
28- \(I=\int_{0}^{3} \frac{x}{(x+1)\sqrt{x+1}}\quad dx\)
29- \(I=\int_{1}^{e^{2}} \frac{\ln (1+\sqrt{x})}{x+\sqrt{x}} \quad dx\)
30- \(I=\int_{\ln (\pi/4)}^{\ln (\pi/2)} e^{2x} \sin \left(e^{x}\right) \quad dx \quad (t=e^{x})\)
31- \(I=\int_{1}^{e}\frac{e^{x}\left(e^{x}+x+1\right)}{\left(e^{x}+1\right)^{2}} \ln x \quad dx\)
32- \(I=\int_{\ln(2)}^{2\ln(2)} \sqrt{e^{x}-1}\quad dx\)
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- \(I=\int_{0}^{\pi} \sqrt{1+\sin x} dx \)