integral from 1 to 3 of ((3x^2-7)/(x^3))

解

\int_{1}^{3} (\frac{3 x ^{2} - 7}{x ^{3}}) d x

3 ln (3) - \frac{28}{9}

十進法表記

0.18472 \dots

解答ステップ

\int_{1}^{3} \frac{3 x ^{2} - 7}{x ^{3}} d x

拡張

\frac{3 x ^{2} - 7}{x ^{3}} : \frac{3}{x} - \frac{7}{x ^{3}}

= \int_{1}^{3} \frac{3}{x} - \frac{7}{x ^{3}} d x

総和規則を適用する:

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

= \int_{1}^{3} \frac{3}{x} d x - \int_{1}^{3} \frac{7}{x ^{3}} d x

\int_{1}^{3} \frac{3}{x} d x = 3 ln (3)

\int_{1}^{3} \frac{7}{x ^{3}} d x = \frac{28}{9}

= 3 ln (3) - \frac{28}{9}