What is the integral of 4e^x-9sin(x) ?

The integral of 4e^x-9sin(x) is 4e^x+9cos(x)+C

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integral of 4e^x-9sin(x)

\int 4 e^{x} - 9 sin (x) d x

4 e^{x} + 9 cos (x) + C

Solution steps

\int 4 e^{x} - 9 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 4 e^{x} d x - \int 9 sin (x) d x

\int 4 e^{x} d x = 4 e^{x}

\int 9 sin (x) d x = - 9 cos (x)

= 4 e^{x} - (- 9 cos (x))

Simplify

= 4 e^{x} + 9 cos (x)

Add a constant to the solution

= 4 e^{x} + 9 cos (x) + C

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What is the integral of 4e^x-9sin(x) ?
The integral of 4e^x-9sin(x) is 4e^x+9cos(x)+C