What is the integral of (2sin(x)-5e^x) ?

The integral of (2sin(x)-5e^x) is -2cos(x)-5e^x+C

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integral of (2sin(x)-5e^x)

\int (2 sin (x) - 5 e^{x}) d x

- 2 cos (x) - 5 e^{x} + C

Solution steps

\int 2 sin (x) - 5 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 2 sin (x) d x - \int 5 e^{x} d x

\int 2 sin (x) d x = - 2 cos (x)

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

= - 2 cos (x) - 5 e^{x}

Add a constant to the solution

= - 2 cos (x) - 5 e^{x} + C

What is the integral of (2sin(x)-5e^x) ?
The integral of (2sin(x)-5e^x) is -2cos(x)-5e^x+C