integral of 12xe^x

解答

\int 12 x e^{x} d x

12 (e^{x} x - e^{x}) + C

求解步骤

\int 12 x e^{x} d x

提出常数:

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

= 12 \cdot \int x e^{x} d x

使用分布积分法

= 12 (e^{x} x - \int e^{x} d x)

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

= 12 (e^{x} x - e^{x})

解答补常数

= 12 (e^{x} x - e^{x}) + C

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