第8章 8.1

(1)

$\int (6x^2-1)dx = 6\cdot\frac{1}{3}x^3 - x + C = 2x^3 - x + C$

(2)

$\int (x^3-5x)dx = \frac{1}{4}x^4 - 5\cdot\frac{1}{2}x^2 + C = \frac{1}{4}x^4 - \frac{5}{2}x^2 + C$

(3)

$\int (2-x)(x-1)dx = \int (-x^2+3x-2)dx = -\frac{1}{3}x^3 + 3\cdot\frac{1}{2}x^2 - 2x + C = -\frac{1}{3}x^3 + \frac{3}{2}x^2 - 2x + C$

(4)

$\int \left(x - \frac{1}{x^2}\right)dx = \frac{1}{2}x^2 - (-1)\frac{1}{x} + C = \frac{1}{2}x^2 + \frac{1}{x} + C$

(5)

$\int (2x - \sqrt{x})dx = 2\cdot\frac{1}{2}x^2 - \frac{2}{3}\sqrt{x^3} + C = x^2 - \frac{2}{3}\sqrt{x^3} + C$

(6)

$\int \left(x - \frac{1}{\sqrt{x}}\right)^2 dx = \int \left(x^2 - 2\sqrt{x} + \frac{1}{x}\right)dx = \frac{1}{3}x^3 - \frac{4}{3}\sqrt{x^3} + \log x + C$