How do you solve the integral from 0 to 1 of x arctan x dx?

Answer 1

The indefinite integral is
(1/2)[(x^2+1)arctanx -x]
Evaluate it at x=1 and subtract the value at x=0

Definite integral = (1/2)[2*(pi/4) -1]
- (1/2)[0 - 0]
= (pi/4) - (1/2)

I used a table of integrals. It looks like a function that requires "integration by parts" .