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

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

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integral of x^2(x+2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{0}^{1} x e^{8 x} d x

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f (x) = sin (2 x), at x = - \frac{π}{3}

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