0-xp-2-x-1-dx-p-R-

Question Number 217813 by Wuji last updated on 21/Mar/25

\underset{0}{\int^{\infty}} [{(x p (2 + x)]}^{- 1} d x

p \in R

Answered by mr W last updated on 22/Mar/25

= \frac{1}{p} \int_{0}^{\infty} \frac{d x}{x (2 + x)}

= \frac{1}{2 p} \int_{0}^{\infty} (\frac{1}{x} - \frac{1}{x + 2}) d x

= \frac{1}{2 p} {[\ln \frac{x}{x + 2}]}_{0}^{\infty}

= \frac{\ln 2}{2 p}

Facebook Tweet Pin