integral from 1 to e of (8x-5/x)

解答

\int_{1}^{e} (8 x - \frac{5}{x}) d x

4 e^{2} - 9

十进制

20.55622 \dots

求解步骤

\int_{1}^{e} 8 x - \frac{5}{x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{e} 8 x d x - \int_{1}^{e} \frac{5}{x} d x

\int_{1}^{e} 8 x d x = 4 (e^{2} - 1)

\int_{1}^{e} \frac{5}{x} d x = 5

= 4 (e^{2} - 1) - 5

化简

4 (e^{2} - 1) - 5 : 4 e^{2} - 9

= 4 e^{2} - 9

\int_{2}^{3} cos (x) d x

\int_{1}^{2} (x - \frac{2}{x})^{2} d x

\int_{0}^{3} 2 π x (x^{2}) d x

\int_{- 1}^{1} (2 x - 1) (2 x + 1) d x

\int_{1}^{3} \frac{x - 6}{x ^{2} ( x + 3 )} d x