integral from 1 to 4 of 4/x-(16)/(x^2)

解答

\int_{1}^{4} \frac{4}{x} - \frac{16}{x ^{2}} d x

8 ln (2) - 12

十进制

- 6.45482 \dots

求解步骤

\int_{1}^{4} \frac{4}{x} - \frac{16}{x ^{2}} 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}^{4} \frac{4}{x} d x - \int_{1}^{4} \frac{16}{x ^{2}} d x

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

\int_{1}^{4} \frac{16}{x ^{2}} d x = 12

= 8 ln (2) - 12

\int cos (\frac{x}{a}) sin (\frac{x}{a}) d x

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