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

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

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

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

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

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

Add a constant to the solution

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

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\int x^{5} sin (x^{6}) d x

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

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