giúp mình với

1. $\int(3x^2 - x + 5)dx$ \[ = \int 3x^2 dx - \int x dx + \int 5 dx = 3 \cdot \frac{x^3}{3} - \frac{x^2}{2} + 5x + C = x^3 - \frac{x^2}{2} + 5x + C \] 2. $\int(4x^5 - x^2 + 1)dx$ \[ = \int 4x^5 dx - \int x^2 dx + \int 1 dx = 4 \cdot \frac{x^6}{6} - \frac{x^3}{3} + x + C = \frac{2x^6}{3} - \frac{x^3}{3} + x + C \] 3. $\int\frac{x^2 - x + 1}{x}dx$ \[ = \int \left( \frac{x^2}{x} - \frac{x}{x} + \frac{1}{x} \right) dx = \int (x - 1 + \frac{1}{x}) dx = \int x dx - \int 1 dx + \int \frac{1}{x} dx = \frac{x^2}{2} - x + \ln|x| + C \] 4. $\int x\sqrt{x}dx$ \[ = \int x \cdot x^{1/2} dx = \int x^{3/2} dx = \frac{x^{5/2}}{5/2} + C = \frac{2x^{5/2}}{5} + C \] 5. $\int(2\sin x - 1)dx$ \[ = \int 2\sin x dx - \int 1 dx = 2(-\cos x) - x + C = -2\cos x - x + C \] 6. $\int(\cos x - \frac{3}{\sin^2 x})dx$ \[ = \int \cos x dx - \int \frac{3}{\sin^2 x} dx = \sin x - 3 \int \csc^2 x dx = \sin x - 3(-\cot x) + C = \sin x + 3\cot x + C \] 7. $\int\frac{x^2 - 3x + 1}{x^3}dx$ \[ = \int \left( \frac{x^2}{x^3} - \frac{3x}{x^3} + \frac{1}{x^3} \right) dx = \int \left( \frac{1}{x} - \frac{3}{x^2} + \frac{1}{x^3} \right) dx = \int \frac{1}{x} dx - 3 \int x^{-2} dx + \int x^{-3} dx = \ln|x| - 3 \cdot \frac{x^{-1}}{-1} + \frac{x^{-2}}{-2} + C = \ln|x| + \frac{3}{x} - \frac{1}{2x^2} + C \] 8. $\int(3\sin x + 5\cos x - 2)dx$ \[ = \int 3\sin x dx + \int 5\cos x dx - \int 2 dx = 3(-\cos x) + 5\sin x - 2x + C = -3\cos x + 5\sin x - 2x + C \]