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

The integral of x^2(5x-3) is 5/3 x^4-x^3-(5x^4)/(12)+C

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integral of x^2(5x-3)

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

\frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{5 x ^{3}}{3} d x = \frac{5 x ^{4}}{12}

= \frac{1}{3} x^{3} (5 x - 3) - \frac{5 x ^{4}}{12}

Expand

\frac{1}{3} x^{3} (5 x - 3) : \frac{5}{3} x^{4} - x^{3}

= \frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12}

Add a constant to the solution

= \frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12} + C

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What is the integral of x^2(5x-3) ?
The integral of x^2(5x-3) is 5/3 x^4-x^3-(5x^4)/(12)+C