Menu Close

Category: Integration

e-1-e-1-ln-x-ln-ln-x-dx-

Question Number 142344 by mnjuly1970 last updated on 30/May/21 $$ \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\underset{\frac{\mathrm{1}}{{e}}} {\int}^{\:{e}} \left\{\frac{\mathrm{1}}{{ln}\left({x}\right)}+{ln}\left({ln}\left({x}\right)\right)\right\}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 30/May/21 $${log}\left({x}\right)={t}…

0-sinx-x-dx-

Question Number 142338 by rs4089 last updated on 30/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{\mu} }{dx}\:\:=?\:\:\: \\ $$ Answered by Dwaipayan Shikari last updated on 30/May/21 $$\frac{\mathrm{1}}{{x}^{\mu} }=\frac{\mathrm{1}}{\Gamma\left(\mu\right)}\int_{\mathrm{0}}…