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

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

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integral of x(2x^2+2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

Add a constant to the solution

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

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