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人気のある微分積分 >

integral of 8x^7e^{4x^8}

解

\int 8 x^{7} e^{4 x^{8}} d x

解

\frac{1}{4} e^{4 x^{8}} + C

解答ステップ

\int 8 x^{7} e^{4 x^{8}} d x

定数を除く:

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

= 8 \cdot \int x^{7} e^{4 x^{8}} d x

u置換積分法を適用する

= 8 \cdot \int \frac{1}{32} d u

定数の積分:

\int a d x = a x

= 8 \cdot \frac{1}{32} u

代用を戻す

u = e^{4 x^{8}}

= 8 \cdot \frac{1}{32} e^{4 x^{8}}

簡素化

8 \cdot \frac{1}{32} e^{4 x^{8}} : \frac{1}{4} e^{4 x^{8}}

= \frac{1}{4} e^{4 x^{8}}

定数を解答に追加する

= \frac{1}{4} e^{4 x^{8}} + C

グラフ

人気の例

integral from 1 to 2 of 1/8 (2+2x-x^2)

\int_{1}^{2} \frac{1}{8} (2 + 2 x - x^{2}) d x

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

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

integral from 0 to 4/3 of pi(4-3x)^2

\int_{0}^{\frac{4}{3}} π (4 - 3 x)^{2} d x

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z \to \frac{1}{2} lim (\frac{3 z + 1}{2 z - 5})

(\partial)/(\partial y)(8xe^{x^2+y^2})

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