What is the integral of (e^x-3cos(x)+2^xe^x) ?

The integral of (e^x-3cos(x)+2^xe^x) is e^x-3sin(x)+((2e)^x)/(ln(2e))+C

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integral of (e^x-3cos(x)+2^xe^x)

\int (e^{x} - 3 cos (x) + 2^{x} e^{x}) d x

e^{x} - 3 sin (x) + \frac{( 2 e ) ^{x}}{ln ( 2 e )} + C

Solution steps

\int e^{x} - 3 cos (x) + 2^{x} 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 e^{x} d x - \int 3 cos (x) d x + \int 2^{x} e^{x} d x

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

\int 3 cos (x) d x = 3 sin (x)

\int 2^{x} e^{x} d x = \frac{( 2 e ) ^{x}}{ln ( 2 e )}

= e^{x} - 3 sin (x) + \frac{( 2 e ) ^{x}}{ln ( 2 e )}

Add a constant to the solution

= e^{x} - 3 sin (x) + \frac{( 2 e ) ^{x}}{ln ( 2 e )} + C

What is the integral of (e^x-3cos(x)+2^xe^x) ?
The integral of (e^x-3cos(x)+2^xe^x) is e^x-3sin(x)+((2e)^x)/(ln(2e))+C