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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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