What is the integral of e^{-2x}+2/(7sqrt(x)) ?

The integral of e^{-2x}+2/(7sqrt(x)) is -1/2 e^{-2x}+4/7 sqrt(x)+C

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integral of e^{-2x}+2/(7sqrt(x))

\int e^{- 2 x} + \frac{2}{7 x} d x

- \frac{1}{2} e^{- 2 x} + \frac{4}{7} x + C

Solution steps

\int e^{- 2 x} + \frac{2}{7 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{- 2 x} d x + \int \frac{2}{7 x} d x

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

\int \frac{2}{7 x} d x = \frac{4}{7} x

= - \frac{1}{2} e^{- 2 x} + \frac{4}{7} x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} + \frac{4}{7} x + C

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What is the integral of e^{-2x}+2/(7sqrt(x)) ?
The integral of e^{-2x}+2/(7sqrt(x)) is -1/2 e^{-2x}+4/7 sqrt(x)+C