integral of e^{-21x}

解答

\int e^{- 21 x} d x

- \frac{1}{21} e^{- 21 x} + C

求解步骤

\int e^{- 21 x} d x

使用换元积分法

= \int - \frac{1}{21} e^{u} d u

提出常数:

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

= - \frac{1}{21} \cdot \int e^{u} d u

使用积分常见定则:

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

= - \frac{1}{21} e^{u}

u = - 21 x

代回

= - \frac{1}{21} e^{- 21 x}

解答补常数

= - \frac{1}{21} e^{- 21 x} + C

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