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人気のある微分積分 >

integral from 0 to x of xe^x

解

\int_{0}^{x} x e^{x} d x

解

e^{x} x - e^{x} + 1

解答ステップ

\int_{0}^{x} x e^{x} d x

部分積分を適用する

= [e^{x} x - \int e^{x} d x]_{0}^{x}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{0}^{x}

限度を計算する:

e^{x} x - e^{x} + 1

= e^{x} x - e^{x} + 1

人気の例

integral from 0 to 7 of e^x

\int_{0}^{7} e^{x} d x

integral from 0 to 2 of (6x-9)(8x^2+4)

\int_{0}^{2} (6 x - 9) (8 x^{2} + 4) d x

integral from 0 to 1 of 2/(1-x^2)

\int_{0}^{1} \frac{2}{1 - x ^{2}} d x

integral from-1 to 0 of x^4

\int_{- 1}^{0} x^{4} d x

integral from 1 to 2 of (v^3+5v^8)/(v^4)

\int_{1}^{2} \frac{v ^{3} + 5 v ^{8}}{v ^{4}} d v