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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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