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

The integral of 3cos(x)+2x+e^x is 3sin(x)+x^2+e^x+C

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

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

3 sin (x) + x^{2} + e^{x} + C

Solution steps

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

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

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

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

= 3 sin (x) + x^{2} + e^{x}

Add a constant to the solution

= 3 sin (x) + x^{2} + e^{x} + C

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