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人気のある微分積分 >

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

解

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

解

\frac{5}{144}

+1

十進法表記

0.03472 \dots

解答ステップ

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

u置換積分法を適用する

= \int_{3}^{4} \frac{u - 2}{u ^{3}} d u

拡張

\frac{u - 2}{u ^{3}} : \frac{1}{u ^{2}} - \frac{2}{u ^{3}}

= \int_{3}^{4} \frac{1}{u ^{2}} - \frac{2}{u ^{3}} 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_{3}^{4} \frac{1}{u ^{2}} d u - \int_{3}^{4} \frac{2}{u ^{3}} d u

\int_{3}^{4} \frac{1}{u ^{2}} d u = \frac{1}{12}

\int_{3}^{4} \frac{2}{u ^{3}} d u = \frac{7}{144}

= \frac{1}{12} - \frac{7}{144}

簡素化

\frac{1}{12} - \frac{7}{144} : \frac{5}{144}

= \frac{5}{144}

グラフ

人気の例

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\int_{- 3}^{\frac{11}{5}} 1 d x

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\int_{1.5}^{4} \frac{1}{8} x d x

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\int_{\frac{1}{4}}^{1} \frac{y + 6}{y ^{2} + 3 y} d y

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

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\int_{1}^{\infty} \frac{9}{x ^{3}} d x