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

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

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

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

e^{x} + x^{2} + 3 x + C

Solution steps

\int e^{x} + 2 x + 3 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 2 x d x + \int 3 d x

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

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

\int 3 d x = 3 x

= e^{x} + x^{2} + 3 x

Add a constant to the solution

= e^{x} + x^{2} + 3 x + C

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