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

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

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integral of x^2(3x-5)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Expand

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

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

Add a constant to the solution

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

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