integral of e^{-0.06t}

解答

\int e^{- 0.06 t} d t

- 16.66666 \dots e^{- 0.06 t} + C

求解步骤

\int e^{- 0.06 t} d t

使用换元积分法

= \int - \frac{1}{0.06} e^{u} d u

提出常数:

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

= - \frac{1}{0.06} \cdot \int e^{u} d u

化简

= - 16.66666 \dots \cdot \int e^{u} d u

使用积分常见定则:

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

= - 16.66666 \dots e^{u}

u = - 0.06 t

代回

= - 16.66666 \dots e^{- 0.06 t}

解答补常数

= - 16.66666 \dots e^{- 0.06 t} + C

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