What is the integral of 1/(sqrt(x))+5e^{-x} ?

The integral of 1/(sqrt(x))+5e^{-x} is 2sqrt(x)-5e^{-x}+C

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integral of 1/(sqrt(x))+5e^{-x}

\int \frac{1}{x} + 5 e^{- x} d x

2 x - 5 e^{- x} + C

Solution steps

\int \frac{1}{x} + 5 e^{- 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 \frac{1}{x} d x + \int 5 e^{- x} d x

\int \frac{1}{x} d x = 2 x

\int 5 e^{- x} d x = - 5 e^{- x}

= 2 x - 5 e^{- x}

Add a constant to the solution

= 2 x - 5 e^{- x} + C

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What is the integral of 1/(sqrt(x))+5e^{-x} ?
The integral of 1/(sqrt(x))+5e^{-x} is 2sqrt(x)-5e^{-x}+C