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

The integral of e^{4x}-6x is 1/4 e^{4x}-3x^2+C

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integral of e^{4x}-6x

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

\frac{1}{4} e^{4 x} - 3 x^{2} + C

Solution steps

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

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

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

= \frac{1}{4} e^{4 x} - 3 x^{2}

Add a constant to the solution

= \frac{1}{4} e^{4 x} - 3 x^{2} + C

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What is the integral of e^{4x}-6x ?
The integral of e^{4x}-6x is 1/4 e^{4x}-3x^2+C