integral of (4-e^{2x})/(e^{2x)}

解答

\int \frac{4 - e ^{2 x}}{e ^{2 x}} d x

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

求解步骤

\int \frac{4 - e ^{2 x}}{e ^{2 x}} d x

乘开

\frac{4 - e ^{2 x}}{e ^{2 x}} : \frac{4}{e ^{2 x}} - 1

= \int \frac{4}{e ^{2 x}} - 1 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 \frac{4}{e ^{2 x}} d x - \int 1 d x

\int \frac{4}{e ^{2 x}} d x = - 2 e^{- 2 x}

\int 1 d x = x

= - 2 e^{- 2 x} - x

解答补常数

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

\int_{0}^{12} \frac{1}{144 + x ^{2}} d x

\frac{\partial}{\partial x} (4 sin (2 x))

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(\frac{π}{x})^{^{'}}

\frac{\partial}{\partial h} (\frac{π}{3} h^{2} (3 r - h))