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## Homework Statement

[tex] \int x \arctan x \, dx [/tex]

## The Attempt at a Solution

By parts,

[tex] u = \arctan x[/tex]

[tex] dv = x dx[/tex]

[tex] du = \frac{dx}{x^2+1}[/tex]

[tex]v = \frac{x^2}{2} [/tex]

[tex] \int x \arctan x \, dx = \frac{x^2}{2}\arctan x - \frac{1}{2} \int \frac{x^2}{x^2+1} \, dx [/tex]

Again...by parts

[tex] u = x^2 [/tex]

[tex] dv = \frac{dx}{x^2+1} [/tex]

[tex] du = 2x dx [/tex]

[tex] v = arc tan x [/tex]

[tex]\int x \arctan x \, dx = \frac{x^2}{2}\arctan x - \frac{x^2}{2}\arctan x - \int x \arctan x \, dx [/tex]

I back to the beginning, what did wrogn?

[tex]\int x \arctan x \, dx = - \int x \arctan x \, dx [/tex]

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