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

The integral of (5x^5+3)x^2 is (5x^8)/8+x^3+C

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integral of (5x^5+3)x^2

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

\frac{5 x ^{8}}{8} + x^{3} + C

Solution steps

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

Expand

(5 x^{5} + 3) x^{2} : 5 x^{7} + 3 x^{2}

= \int 5 x^{7} + 3 x^{2} 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 5 x^{7} d x + \int 3 x^{2} d x

\int 5 x^{7} d x = \frac{5 x ^{8}}{8}

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

= \frac{5 x ^{8}}{8} + x^{3}

Add a constant to the solution

= \frac{5 x ^{8}}{8} + x^{3} + C

What is the integral of (5x^5+3)x^2 ?
The integral of (5x^5+3)x^2 is (5x^8)/8+x^3+C