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

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

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

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

\frac{1}{3} x^{3} (5 + 2 x^{3}) - \frac{x ^{6}}{3} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} (5 + 2 x^{3}) - \int 2 x^{5} d x

= \frac{1}{3} x^{3} (5 + 2 x^{3}) - \int 2 x^{5} d x

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

= \frac{1}{3} x^{3} (5 + 2 x^{3}) - \frac{x ^{6}}{3}

Add a constant to the solution

= \frac{1}{3} x^{3} (5 + 2 x^{3}) - \frac{x ^{6}}{3} + C

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