What is the integral of (x^2+x^3)x ?

The integral of (x^2+x^3)x is (x^4)/4+(x^5)/5+C

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integral of (x^2+x^3)x

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

\frac{x ^{4}}{4} + \frac{x ^{5}}{5} + C

Solution steps

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

Expand

(x^{2} + x^{3}) x : x^{3} + x^{4}

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

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

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{x ^{4}}{4} + \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{x ^{5}}{5} + C

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What is the integral of (x^2+x^3)x ?
The integral of (x^2+x^3)x is (x^4)/4+(x^5)/5+C