What is the integral of 5e^x-7sin(x) ?

The integral of 5e^x-7sin(x) is 5e^x+7cos(x)+C

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integral of 5e^x-7sin(x)

\int 5 e^{x} - 7 sin (x) d x

5 e^{x} + 7 cos (x) + C

Solution steps

\int 5 e^{x} - 7 sin (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 5 e^{x} d x - \int 7 sin (x) d x

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

\int 7 sin (x) d x = - 7 cos (x)

= 5 e^{x} - (- 7 cos (x))

Simplify

= 5 e^{x} + 7 cos (x)

Add a constant to the solution

= 5 e^{x} + 7 cos (x) + C

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What is the integral of 5e^x-7sin(x) ?
The integral of 5e^x-7sin(x) is 5e^x+7cos(x)+C