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

The integral of x^3(2-x^2) is 1/4 x^4(2-x^2)+(x^6)/(12)+C

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integral of x^3(2-x^2)

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

\frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{4} x^{4} (2 - x^{2}) - \int - \frac{x ^{5}}{2} d x

= \frac{1}{4} x^{4} (2 - x^{2}) - \int - \frac{x ^{5}}{2} d x

\int - \frac{x ^{5}}{2} d x = - \frac{x ^{6}}{12}

= \frac{1}{4} x^{4} (2 - x^{2}) - (- \frac{x ^{6}}{12})

Simplify

= \frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12}

Add a constant to the solution

= \frac{1}{4} x^{4} (2 - x^{2}) + \frac{x ^{6}}{12} + C

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What is the integral of x^3(2-x^2) ?
The integral of x^3(2-x^2) is 1/4 x^4(2-x^2)+(x^6)/(12)+C