What is the integral of 2e^x+sin(7x) ?

The integral of 2e^x+sin(7x) is 2e^x-1/7 cos(7x)+C

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integral of 2e^x+sin(7x)

\int 2 e^{x} + sin (7 x) d x

2 e^{x} - \frac{1}{7} cos (7 x) + C

Solution steps

\int 2 e^{x} + sin (7 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 2 e^{x} d x + \int sin (7 x) d x

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

\int sin (7 x) d x = - \frac{1}{7} cos (7 x)

= 2 e^{x} - \frac{1}{7} cos (7 x)

Add a constant to the solution

= 2 e^{x} - \frac{1}{7} cos (7 x) + C

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What is the integral of 2e^x+sin(7x) ?
The integral of 2e^x+sin(7x) is 2e^x-1/7 cos(7x)+C