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

The integral of cos(5x)+e^x is 1/5 sin(5x)+e^x+C

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integral of cos(5x)+e^x

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

\frac{1}{5} sin (5 x) + e^{x} + C

Solution steps

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

\int cos (5 x) d x = \frac{1}{5} sin (5 x)

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

= \frac{1}{5} sin (5 x) + e^{x}

Add a constant to the solution

= \frac{1}{5} sin (5 x) + e^{x} + C

What is the integral of cos(5x)+e^x ?
The integral of cos(5x)+e^x is 1/5 sin(5x)+e^x+C