integral of xe^{-3}

解答

\int x e^{- 3} d x

\frac{x ^{2}}{2 e ^{3}} + C

求解步骤

\int x e^{- 3} d x

提出常数:

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

= e^{- 3} \cdot \int x d x

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{3}} \cdot \int x d x

使用幂法则

= \frac{1}{e ^{3}} \cdot \frac{x ^{2}}{2}

化简

\frac{1}{e ^{3}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e ^{3}}

= \frac{x ^{2}}{2 e ^{3}}

解答补常数

= \frac{x ^{2}}{2 e ^{3}} + C

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