integral from 0 to ln(6) of e^x-e^{-3x}

解答

\int_{0}^{l n (6)} e^{x} - e^{- 3 x} d x

\frac{3025}{648}

十进制

4.66820 \dots

求解步骤

\int_{0}^{l n (6)} e^{x} - e^{- 3 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_{0}^{l n (6)} e^{x} d x - \int_{0}^{l n (6)} e^{- 3 x} d x

\int_{0}^{l n (6)} e^{x} d x = 5

\int_{0}^{l n (6)} e^{- 3 x} d x = \frac{215}{648}

= 5 - \frac{215}{648}

化简

5 - \frac{215}{648} : \frac{3025}{648}

= \frac{3025}{648}

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