What is the integral of (x+e^{5x}) ?

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

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integral of (x+e^{5x})

\int (x + e^{5 x}) d x

\frac{x ^{2}}{2} + \frac{1}{5} e^{5 x} + C

Solution steps

\int x + e^{5 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 x d x + \int e^{5 x} d x

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

\int e^{5 x} d x = \frac{1}{5} e^{5 x}

= \frac{x ^{2}}{2} + \frac{1}{5} e^{5 x}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{1}{5} e^{5 x} + C

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