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人気のある微分積分 >

integral from 1 to 4 of (x^5-x)/(3x^3)

解

\int_{1}^{4} \frac{x ^{5} - x}{3 x ^{3}} d x

解

\frac{27}{4}

+1

十進法表記

6.75

解答ステップ

\int_{1}^{4} \frac{x ^{5} - x}{3 x ^{3}} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{1}^{4} \frac{x ^{5} - x}{x ^{3}} d x

拡張

\frac{x ^{5} - x}{x ^{3}} : x^{2} - \frac{1}{x ^{2}}

= \frac{1}{3} \cdot \int_{1}^{4} x^{2} - \frac{1}{x ^{2}} 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

= \frac{1}{3} (\int_{1}^{4} x^{2} d x - \int_{1}^{4} \frac{1}{x ^{2}} d x)

\int_{1}^{4} x^{2} d x = 21

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

= \frac{1}{3} (21 - \frac{3}{4})

簡素化

\frac{1}{3} (21 - \frac{3}{4}) : \frac{27}{4}

= \frac{27}{4}

グラフ

人気の例

integral from 1 to 2 of 3/7 x^3

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

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\int_{0}^{2 π} (sin (4 x))^{2} d x

integral from 4 to 6 of x^2sqrt(x-4)

\int_{4}^{6} x^{2} x - 4 d x

integral from 2 to 4 of (xy^2+x^2+y+4)

\int_{2}^{4} (x y^{2} + x^{2} + y + 4) d y

integral from-5 to-3 of sqrt(x^2-4)

\int_{- 5}^{- 3} x^{2} - 4 d x