Cầnn gấpp ạ

1. $\int(7x-3)dx$ \[ = \int 7x dx - \int 3 dx = 7 \cdot \frac{x^2}{2} - 3x + C = \frac{7x^2}{2} - 3x + C \] 2. $\int\frac{5-x+\sqrt x}{\sqrt[3]{x^2}}dx$ \[ = \int \left( \frac{5}{x^{2/3}} - \frac{x}{x^{2/3}} + \frac{x^{1/2}}{x^{2/3}} \right) dx = \int \left( 5x^{-2/3} - x^{1/3} + x^{-1/6} \right) dx = 5 \cdot \frac{x^{1/3}}{1/3} - \frac{x^{4/3}}{4/3} + \frac{x^{5/6}}{5/6} + C = 15x^{1/3} - \frac{3x^{4/3}}{4} + \frac{6x^{5/6}}{5} + C \] 3. $\int(\frac{3}{x} - 2x)dx$ \[ = \int \frac{3}{x} dx - \int 2x dx = 3 \ln |x| - x^2 + C \] 4. $\int\frac{x^2-2x+1}{2x-1}dx$ \[ = \int \left( \frac{x^2}{2x-1} - \frac{2x}{2x-1} + \frac{1}{2x-1} \right) dx = \int \left( \frac{x^2}{2x-1} - 1 + \frac{1}{2x-1} \right) dx = \int \left( \frac{x^2}{2x-1} - 1 + \frac{1}{2x-1} \right) dx = \frac{x^2}{2} - x + \frac{1}{2} \ln |2x-1| + C \] 5. $\int\frac{5x^4+3x-3}{x^2}dx$ \[ = \int \left( \frac{5x^4}{x^2} + \frac{3x}{x^2} - \frac{3}{x^2} \right) dx = \int \left( 5x^2 + \frac{3}{x} - \frac{3}{x^2} \right) dx = 5 \cdot \frac{x^3}{3} + 3 \ln |x| + \frac{3}{x} + C = \frac{5x^3}{3} + 3 \ln |x| + \frac{3}{x} + C \] 6. $\int\frac{(x^2-2)^2}{x^2}dx$ \[ = \int \left( \frac{x^4 - 4x^2 + 4}{x^2} \right) dx = \int \left( x^2 - 4 + \frac{4}{x^2} \right) dx = \frac{x^3}{3} - 4x - \frac{4}{x} + C \] 7. $\int(\frac{1}{\sqrt x} - \frac{3}{\sqrt[3]{x}} + x)dx$ \[ = \int \left( x^{-1/2} - 3x^{-1/3} + x \right) dx = 2x^{1/2} - 3 \cdot \frac{x^{2/3}}{2/3} + \frac{x^2}{2} + C = 2x^{1/2} - \frac{9x^{2/3}}{2} + \frac{x^2}{2} + C \] 8. $\int(2\sqrt x - 3\sqrt[3]{x^2} - 2)dx$ \[ = \int \left( 2x^{1/2} - 3x^{2/3} - 2 \right) dx = 2 \cdot \frac{x^{3/2}}{3/2} - 3 \cdot \frac{x^{5/3}}{5/3} - 2x + C = \frac{4x^{3/2}}{3} - \frac{9x^{5/3}}{5} - 2x + C \] 9. $\int\frac{x-4}{\sqrt[3]{x}}dx$ \[ = \int \left( x^{2/3} - 4x^{-1/3} \right) dx = \frac{x^{5/3}}{5/3} - 4 \cdot \frac{x^{2/3}}{2/3} + C = \frac{3x^{5/3}}{5} - 6x^{2/3} + C \] 10. $\int\frac{3x^2-\sqrt x+\sqrt[3]x}{x}dx$ \[ = \int \left( 3x - x^{-1/2} + x^{-2/3} \right) dx = \frac{3x^2}{2} - 2x^{1/2} + \frac{3x^{1/3}}{1/3} + C = \frac{3x^2}{2} - 2x^{1/2} + 3x^{1/3} + C \] 11. $\int\sin2xdx$ \[ = -\frac{\cos 2x}{2} + C \] 12. $\int\sin2x.\cos3xdx$ \[ = \int \left( \frac{1}{2} (\sin 5x - \sin x) \right) dx = \frac{1}{2} \left( -\frac{\cos 5x}{5} + \cos x \right) + C = -\frac{\cos 5x}{10} + \frac{\cos x}{2} + C \] 13. $\int\sin(2x+1)dx$ \[ = -\frac{\cos (2x+1)}{2} + C \] 14. $\int2\sin^2\frac{x}{2}dx$ \[ = \int (1 - \cos x) dx = x - \sin x + C \] 15. $\int\frac{dx}{(3-2x)^5}$ \[ = -\frac{1}{8(3-2x)^4} + C \] 16. $\int\frac{dx}{x^2-3x+2}$ \[ = \int \left( \frac{1}{x-1} - \frac{1}{x-2} \right) dx = \ln |x-1| - \ln |x-2| + C = \ln \left| \frac{x-1}{x-2} \right| + C \] 17. $\int\frac{x}{(x+2)^2}dx$ \[ = \int \left( \frac{1}{x+2} - \frac{2}{(x+2)^2} \right) dx = \ln |x+2| + \frac{2}{x+2} + C \] 18. $\int\frac{4\sin^3x}{1+\cos x}dx$ \[ = \int \left( 4 \sin x \cdot \frac{1 - \cos^2 x}{1 + \cos x} \right) dx = \int \left( 4 \sin x (1 - \cos x) \right) dx = -4 \cos x + 4 \sin x + C \] 19. $\int\frac{x^3}{x+2}dx$ \[ = \int \left( x^2 - 2x + 4 - \frac{8}{x+2} \right) dx = \frac{x^3}{3} - x^2 + 4x - 8 \ln |x+2| + C \] 20. $\int\frac{3xdx}{x^2-5x+4}$ \[ = \int \left( \frac{3}{x-1} - \frac{3}{x-4} \right) dx = 3 \ln |x-1| - 3 \ln |x-4| + C = 3 \ln \left| \frac{x-1}{x-4} \right| + C \] 21. $\int(\tan x - \cot x)^2dx$ \[ = \int \left( \tan^2 x - 2 \tan x \cot x + \cot^2 x \right) dx = \int \left( \sec^2 x - 2 + \csc^2 x \right) dx = \tan x - 2x - \cot x + C \] 22. $\int\frac{2^{x-3} - 1}{e^x}dx$ \[ = \int \left( 2^{x-3} e^{-x} - e^{-x} \right) dx = \int \left( 2^{x-3} e^{-x} - e^{-x} \right) dx = \frac{2^{x-3} e^{-x}}{\ln 2 - 1} + e^{-x} + C \] 23. $\int\frac{2x+1}{(x-1)(x+1)}dx$ \[ = \int \left( \frac{3}{2(x-1)} + \frac{1}{2(x+1)} \right) dx = \frac{3}{2} \ln |x-1| + \frac{1}{2} \ln |x+1| + C \] 24. $\int e^{2x-3}dx$ \[ = \frac{e^{2x-3}}{2} + C \] 25. $\int e^x \left( 4 + \frac{e^{-x}}{\cos^2 x} \right) dx$ \[ = \int \left( 4e^x + \frac{1}{\cos^2 x} \right) dx = 4e^x + \tan x + C \] 26. $\int 2^{3x+1} dx$ \[ = \frac{2^{3x+1}}{3 \ln 2} + C \] 27. $\int \frac{\cos^3 x}{1 + \sin x} dx$ \[ = \int \left( \cos^2 x \cdot \frac{\cos x}{1 + \sin x} \right) dx = \int \left( (1 - \sin^2 x) \cdot \frac{\cos x}{1 + \sin x} \right) dx = \int \left( \frac{\cos x}{1 + \sin x} - \sin x \cos x \right) dx = \ln |1 + \sin x| - \frac{\sin^2 x}{2} + C \] 28. $\int \cos^3 x \sin x dx$ \[ = \int \cos^3 x \sin x dx = -\frac{\cos^4 x}{4} + C \] 29. $\int \tan^2 x dx$ \[ = \int (\sec^2 x - 1) dx = \tan x - x + C \] 30. $\int \frac{e^{3x+1}}{4^x} dx$ \[ = \int \left( e^{3x+1} \cdot 4^{-x} \right) dx = \int \left( e^{3x+1} \cdot e^{-2x \ln 2} \right) dx = \int \left( e^{(3 - 2 \ln 2)x + 1} \right) dx = \frac{e^{(3 - 2 \ln 2)x + 1}}{3 - 2 \ln 2} + C \]