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Popular >

integral of uarctan(u)

Solution

\int u arctan (u) d u

Solution

\frac{1}{2} u^{2} arctan (u) - \frac{1}{2} (- arctan (u) + u) + C

Solution steps

\int u arctan (u) d u

Apply Integration By Parts

: \frac{1}{2} u^{2} arctan (u) - \int \frac{u ^{2}}{2 ( u ^{2} + 1 )} d u

= \frac{1}{2} u^{2} arctan (u) - \int \frac{u ^{2}}{2 ( u ^{2} + 1 )} d u

\int \frac{u ^{2}}{2 ( u ^{2} + 1 )} d u = \frac{1}{2} (- arctan (u) + u)

= \frac{1}{2} u^{2} arctan (u) - \frac{1}{2} (- arctan (u) + u)

Add a constant to the solution

= \frac{1}{2} u^{2} arctan (u) - \frac{1}{2} (- arctan (u) + u) + C

Popular Examples

integral of (x/(sqrt(2x^2+3)))

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

integral of 2/(5-2x)

\int \frac{2}{5 - 2 x} d x

integral of 9e^z

\int 9 e^{z} d z

integral of sin(x)(tan(x)-cot(x))^2

\int sin (x) (tan (x) - cot (x))^{2} d x

integral of 5sec^2(2x)

\int 5 sec^{2} (2 x) d x

Frequently Asked Questions (FAQ)

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