integral of xe^x+x

解答

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

e^{x} x - e^{x} + \frac{x ^{2}}{2} + C

求解步骤

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

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= e^{x} x - e^{x} + \frac{x ^{2}}{2}

解答补常数

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

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