1-e-e-arctan-x-x-dx-

Question Number 204909 by mnjuly1970 last updated on 01/Mar/24

Ω = \int_{\frac{1}{e}}^{e} \frac{a r c t a n (x)}{x} d x = ?

Answered by witcher3 last updated on 01/Mar/24

x \to \frac{1}{x}

Ω = \int_{\frac{1}{e}}^{e} \frac{\tan^{- 1} (\frac{1}{x})}{\frac{1}{x}} . \frac{1}{x^{2}} = \int_{\frac{1}{e}}^{e} \frac{\frac{π}{2} - \tan^{- 1} (x)}{x} = \frac{π}{2} \ln (e^{2}) - Ω

Ω = \frac{π}{2}

Commented by mnjuly1970 last updated on 01/Mar/24

⋚

Commented by witcher3 last updated on 01/Mar/24

withe Pleasur Sir