integral of (2x+3)e^x

解答

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

2 e^{x} x + e^{x} + C

求解步骤

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

使用分布积分法

= (2 x + 3) e^{x} - \int 2 e^{x} d x

\int 2 e^{x} d x = 2 e^{x}

= (2 x + 3) e^{x} - 2 e^{x}

化简

(2 x + 3) e^{x} - 2 e^{x} : 2 e^{x} x + e^{x}

= 2 e^{x} x + e^{x}

解答补常数

= 2 e^{x} x + e^{x} + C

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