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人気のある微分積分 >

integral from 0 to 15 of x/((1+x)^{3/4)}

解

\int_{0}^{15} \frac{x}{( 1 + x ) ^{\frac{3}{4}}} d x

解

\frac{104}{5}

+1

十進法表記

20.8

解答ステップ

\int_{0}^{15} \frac{x}{( 1 + x ) ^{\frac{3}{4}}} d x

u置換積分法を適用する

= \int_{1}^{16} \frac{u - 1}{u ^{\frac{3}{4}}} d u

拡張

\frac{u - 1}{u ^{\frac{3}{4}}} : u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}}

= \int_{1}^{16} u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}} d u

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}^{16} u^{\frac{1}{4}} d u - \int_{1}^{16} \frac{1}{u ^{\frac{3}{4}}} d u

\int_{1}^{16} u^{\frac{1}{4}} d u = \frac{124}{5}

\int_{1}^{16} \frac{1}{u ^{\frac{3}{4}}} d u = 4

= \frac{124}{5} - 4

簡素化

\frac{124}{5} - 4 : \frac{104}{5}

= \frac{104}{5}

グラフ

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