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

\int y^{2} e^{y^{2}} d y

n = 1 \sum \infty (\frac{1}{10})^{n}

\frac{d}{d x} ((x + 1)^{e^{x}})

\frac{d}{d x} (cos (x) x^{- 2})

\frac{\partial}{\partial x} (\frac{3 y ^{2}}{x})

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