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

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

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

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

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

Solution steps

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

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

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

= 2 x - (- \frac{1}{2} e^{- 2 x})

Simplify

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

Add a constant to the solution

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

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