integral of xe^xln(2)

解答

\int x e^{x} ln (2) d x

ln (2) (e^{x} x - e^{x}) + C

求解步骤

\int x e^{x} ln (2) d x

提出常数:

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

= ln (2) \cdot \int x e^{x} d x

使用分布积分法

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

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

= ln (2) (e^{x} x - e^{x})

解答补常数

= ln (2) (e^{x} x - e^{x}) + C