What is the integral of sin(x)+e^{2x} ?

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

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integral of sin(x)+e^{2x}

\int sin (x) + e^{2 x} d x

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

Solution steps

\int sin (x) + 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 sin (x) d x + \int e^{2 x} d x

\int sin (x) d x = - cos (x)

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

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

Add a constant to the solution

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

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