integral from 1 to 5 of (3x^{-1}+x^{-3})

解

\int_{1}^{5} (3 x^{- 1} + x^{- 3}) d x

3 ln (5) + \frac{12}{25}

十進法表記

5.30831 \dots

解答ステップ

\int_{1}^{5} 3 x^{- 1} + x^{- 3} d x

簡素化

3 x^{- 1} + x^{- 3} : \frac{3}{x} + \frac{1}{x ^{3}}

= \int_{1}^{5} \frac{3}{x} + \frac{1}{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}^{5} \frac{3}{x} d x + \int_{1}^{5} \frac{1}{x ^{3}} d x

\int_{1}^{5} \frac{3}{x} d x = 3 ln (5)

\int_{1}^{5} \frac{1}{x ^{3}} d x = \frac{12}{25}

= 3 ln (5) + \frac{12}{25}