0-oo-artan-2x-arctan-x-x-dx-

Question Number 184626 by SANOGO last updated on 09/Jan/23

\int_{0}^{+ o o} \frac{a r t a n (2 x) - a r c t a n (x)}{x} d x

Answered by qaz last updated on 10/Jan/23

\int_{0}^{\infty} \frac{\arctan 2 x - \arctan x}{x} d x

= \int_{0}^{\infty} \int_{1}^{2} \frac{1}{1 + a^{2} x^{2}} d a d x = \int_{1}^{2} d a \int_{0}^{\infty} \frac{d x}{1 + a^{2} x^{2}}

= \int_{1}^{2} \frac{π}{2 a} d a = \frac{π}{2} l n 2

Facebook Tweet Pin