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

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

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integral of 1/(2sqrt(x))+e^{-x}

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

x - e^{- x} + C

Solution steps

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

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

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

= x - e^{- x}

Add a constant to the solution

= x - e^{- x} + C

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