What is the integral of 4e^{2x}+x^2 ?

The integral of 4e^{2x}+x^2 is 2e^{2x}+(x^3)/3+C

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integral of 4e^{2x}+x^2

\int 4 e^{2 x} + x^{2} d x

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

Solution steps

\int 4 e^{2 x} + x^{2} 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^{2 x} d x + \int x^{2} d x

\int 4 e^{2 x} d x = 2 e^{2 x}

\int x^{2} d x = \frac{x ^{3}}{3}

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

Add a constant to the solution

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

What is the integral of 4e^{2x}+x^2 ?
The integral of 4e^{2x}+x^2 is 2e^{2x}+(x^3)/3+C