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Integral Calculus

logx.dx/x integrate where limit is from 4 to 8

Bilal

12 Years agoGrade

1 Answer

Sher Mohammad

12 Years ago

$\int_a^b \frac{\log (x)}{x} \, dx$ = $\left[\frac{1}{2} \left(\log ^2(b)-\log ^2(a)\right),\Re(a)\geq 0\land \Re(b)\geq 0\land \left(\left(\Re\left(\frac{a}{b-a}\right)\geq 0\land a^2\neq a b\right)\lor \frac{a}{a-b}\notin \mathbb{R}\lor \Re\left(\frac{a}{a-b}\right)>1\right)\right]$

$\int_4^8 \frac{\log (x)}{x} \, dx$ =(5 Log[2]^2)/2

Sher Mohammad

B.tech, IIT Delhi

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