What is the integral of (3x^2+1)arctan(x) ?

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

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integral of (3x^2+1)arctan(x)

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

arctan (x) (x^{3} + x) - \frac{x ^{2}}{2} + C

Solution steps

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

Apply Integration By Parts

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

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

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

= arctan (x) (x^{3} + x) - \frac{x ^{2}}{2}

Add a constant to the solution

= arctan (x) (x^{3} + x) - \frac{x ^{2}}{2} + C

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