Задачи для самостоятельного решения

Базовые методы интегрирования
1. $$\int (x^2 +2\sin x -4)\,dx$$
2. $$\int (x^{-2}-5\sqrt{x}+\frac{1}{x^4})\,dx$$
3. $$\int (\sin 2x-4\cos^2 x+\pi)\,dx$$
4. $$\int \displaystyle\frac{1}{x^2+5}\,dx$$+$$\int \displaystyle\frac{\sqrt{x}-x^3e^x+x^2}{x^3}\,dx$$
5. $$\int \displaystyle\frac{1}{\sqrt{3-3x^2}}\,dx$$
6. $$\int \displaystyle\frac{3\cdot 2^x-2\cdot 3^x}{2^x}\,dx$$
7. $$\int \displaystyle\frac{1+2x^2}{x^2 (1+x^2)}\,dx$$
8. $$\int ((3x+1)^{15}-\sin (2013x))\,dx$$
9. $$\int \displaystyle\frac{x}{\sqrt{9-x^4}}\,dx$$
10. $$\int \displaystyle\frac{x^2}{x^6+4}\,dx$$
11. $$\int \displaystyle\frac{1}{\sqrt{1+tgx}\cos^2 x}\,dx$$
12. $$\int \displaystyle\frac{x(1-x^2)}{2+x^4}\,dx$$
13. $$\int \displaystyle\frac{2x-1}{x-2}\,dx$$
14. $$\int \sqrt{\frac{1-x}{1+x}}\,dx$$
15. $$\int (\cos^3 x\cdot \sin 2x)\,dx$$

Метод замены переменной. Метод интегрирования по частям

1. $$\int \displaystyle\frac{1}{x+\sqrt{x}}\,dx$$
2. $$\int \displaystyle\frac{1}{x\sqrt{4-x^2}}\,dx$$
3. $$\int \displaystyle\frac{1}{\sqrt{3+e^x}}\,dx$$
4. $$\int \displaystyle\frac{\sin^3 x}{\cos^4 x}\,dx$$
5. $$\int (x^2+1)e^{-2x}\,dx$$
6. $$\int (x^2+x-3)\sin 3x\,dx$$
7. $$\int e^{nx}\cos (mx)\,dx$$
8. $$\int \displaystyle\frac{\sqrt{x}}{\sqrt{x}-\sqrt[3]{x}}\,dx$$
9. $$\int \displaystyle\frac{ e^{2x} }{ \sqrt[4]{e^x+1} }\,dx$$
10. $$\int (2x+3)\ln (x-2)\,dx$$
11. $$\int \arcsin^2 x\,dx$$
12. $$\int \displaystyle\frac{\arccos \sqrt{x}}{\sqrt{x-1}}\,dx$$
13. $$\int \cos (\ln x)\,dx$$
14. $$\int \displaystyle\frac{\sin^2 x}{e^x}\,dx$$
15. $$\int \displaystyle\frac{x\cos x}{\sin^2 x}\,dx$$