integral of (-2x)/(e^x)

解答

\int \frac{- 2 x}{e ^{x}} d x

- 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

求解步骤

\int \frac{- 2 x}{e ^{x}} d x

提出常数:

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

= - 2 \cdot \int \frac{x}{e ^{x}} d x

使用分布积分法

= - 2 (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

\int - \frac{1}{e ^{x}} d x = \frac{1}{e ^{x}}

= - 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

解答补常数

= - 2 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

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