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

The integral of x(3x-2)^2 is 9/2 x^4-(9x^4)/4-4x^3+2x^2+C

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integral of x(3x-2)^2

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

\frac{9}{2} x^{4} - \frac{9 x ^{4}}{4} - 4 x^{3} + 2 x^{2} + C

Solution steps

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

Apply Integration By Parts

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

\int 3 x^{2} (3 x - 2) d x = \frac{9 x ^{4}}{4} - 2 x^{3}

= \frac{1}{2} x^{2} (3 x - 2)^{2} - (\frac{9 x ^{4}}{4} - 2 x^{3})

Simplify

\frac{1}{2} x^{2} (3 x - 2)^{2} - (\frac{9 x ^{4}}{4} - 2 x^{3}) : \frac{9}{2} x^{4} - \frac{9 x ^{4}}{4} - 4 x^{3} + 2 x^{2}

= \frac{9}{2} x^{4} - \frac{9 x ^{4}}{4} - 4 x^{3} + 2 x^{2}

Add a constant to the solution

= \frac{9}{2} x^{4} - \frac{9 x ^{4}}{4} - 4 x^{3} + 2 x^{2} + C

What is the integral of x(3x-2)^2 ?
The integral of x(3x-2)^2 is 9/2 x^4-(9x^4)/4-4x^3+2x^2+C