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

The integral of x^2(x+2/3) is 1/9 x^3(3x+2)-(x^4)/(12)+C

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

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

\frac{1}{9} x^{3} (3 x + 2) - \frac{x ^{4}}{12} + C

Solution steps

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

Apply Integration By Parts

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

= \frac{1}{9} x^{3} (3 x + 2) - \int \frac{x ^{3}}{3} d x

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

= \frac{1}{9} x^{3} (3 x + 2) - \frac{x ^{4}}{12}

Add a constant to the solution

= \frac{1}{9} x^{3} (3 x + 2) - \frac{x ^{4}}{12} + C

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What is the integral of x^2(x+2/3) ?
The integral of x^2(x+2/3) is 1/9 x^3(3x+2)-(x^4)/(12)+C