What is the integral of (e^y-e^{2x}) ?

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

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integral of (e^y-e^{2x})

\int (e^{y} - e^{2 x}) d x

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

Solution steps

\int e^{y} - 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 e^{2 x} d x + \int e^{y} d x

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

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

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

Add a constant to the solution

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

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