Tính các tích phân sau

1.I=\(\int\limits^{\frac{\Pi}{4}}_0\) (x+1)sin2xdx

2.I=\(\int\limits^2_1\frac{x^2+3x+1}{x^2+x}dx\)

3.I=\(\int\limits^2_1\frac{x^2-1}{x^2}lnxdx\)

4. I=\(\int\limits^1_0x\sqrt{2-x^2}dx\)

5.I=\(\int\limits^1_0\frac{\left(x+1\right)^2}{x^2+1}dx\)

6. I=\(\int\limits^5_1\frac{dx}{1+\sqrt{2x-1}}\)

7. I=\(\int\limits^3_1\frac{1+ln\left(x+1\right)}{x^2}dx\)

8.I=\(\int\limits^1_0\frac{x^3}{x^4+3x^2+2}dx\)

9. I=\(\int\limits^{\frac{\Pi}{4}}_0x\left(1+sin2x\right)dx\)

10. I=\(\int\limits^3_0\frac{x}{\sqrt{x+1}}dx\)

Tìm các nguyên hàm sau

1.\(\int\frac{9x^2}{\sqrt{1-x^3}}dx\)

2.\(\int\frac{1}{\sqrt{x}\left(1+\sqrt{x}\right)^3}dx\)

3.\(\int\frac{x}{\sqrt{2x+3}}dx\)

4.\(\int\) \(\frac{e^{2x}}{\sqrt{1+e^x}}\) dx

5.\(\int\frac{\sqrt[3]{1+lnx}}{x}dx\)

6.\(\int\) cosxsin³xdx

7.\(\int\) (x²+2x-1)e^xdx

8.\(\int\) e^xcosxdx

9.\(\int\) xsin(2x+1)dx

10.\(\int\) (1-2x)e^3xdx