What is the integral of 3x^2-4-6e^{2x} ?

The integral of 3x^2-4-6e^{2x} is x^3-4x-3e^{2x}+C

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integral of 3x^2-4-6e^{2x}

\int 3 x^{2} - 4 - 6 e^{2 x} d x

x^{3} - 4 x - 3 e^{2 x} + C

Solution steps

\int 3 x^{2} - 4 - 6 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 4 d x - \int 6 e^{2 x} d x

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

\int 4 d x = 4 x

\int 6 e^{2 x} d x = 3 e^{2 x}

= x^{3} - 4 x - 3 e^{2 x}

Add a constant to the solution

= x^{3} - 4 x - 3 e^{2 x} + C

\int x^{\frac{1}{3}} (2 x + 3) d x

\int \frac{4}{x + 1} d x

\int \frac{1}{e ^{3 x} + 1} d x

\int cos (2 n) x d x

\int x (x - 5)^{2} (x + 1) d x

What is the integral of 3x^2-4-6e^{2x} ?
The integral of 3x^2-4-6e^{2x} is x^3-4x-3e^{2x}+C