What is the integral of 3x^2-3-4e^{2x} ?

The integral of 3x^2-3-4e^{2x} is x^3-3x-2e^{2x}+C

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integral of 3x^2-3-4e^{2x}

\int 3 x^{2} - 3 - 4 e^{2 x} d x

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

Solution steps

\int 3 x^{2} - 3 - 4 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 3 d x - \int 4 e^{2 x} d x

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

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

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