What is the integral of-e^{4x}+4x^5 ?

The integral of-e^{4x}+4x^5 is -1/4 e^{4x}+(2x^6)/3+C

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integral of-e^{4x}+4x^5

\int - e^{4 x} + 4 x^{5} d x

- \frac{1}{4} e^{4 x} + \frac{2 x ^{6}}{3} + C

Solution steps

\int - e^{4 x} + 4 x^{5} 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 4 x^{5} d x

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

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

= - \frac{1}{4} e^{4 x} + \frac{2 x ^{6}}{3}

Add a constant to the solution

= - \frac{1}{4} e^{4 x} + \frac{2 x ^{6}}{3} + C

What is the integral of-e^{4x}+4x^5 ?
The integral of-e^{4x}+4x^5 is -1/4 e^{4x}+(2x^6)/3+C