What is the integral of (2x^3+5)x ?

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

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integral of (2x^3+5)x

\int (2 x^{3} + 5) x d x

\frac{2 x ^{5}}{5} + \frac{5 x ^{2}}{2} + C

Solution steps

\int (2 x^{3} + 5) x d x

Expand

(2 x^{3} + 5) x : 2 x^{4} + 5 x

= \int 2 x^{4} + 5 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 2 x^{4} d x + \int 5 x d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{2 x ^{5}}{5} + \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{2 x ^{5}}{5} + \frac{5 x ^{2}}{2} + C

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