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Category: Integration

please-help-me-calculate-I-2-1-e-2-12288ln-x-1-ln-12-x-1-4096-x-1-dx-thanks-

Question Number 46087 by Saorey last updated on 21/Oct/18 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}!! \\ $$$$\mathrm{calculate}: \\ $$$$\mathrm{I}=\underset{\mathrm{2}} {\overset{\mathrm{1}+\mathrm{e}^{\mathrm{2}} } {\int}}\frac{\mathrm{12288ln}\left(\mathrm{x}−\mathrm{1}\right)}{\left[\mathrm{ln}^{\mathrm{12}} \left(\mathrm{x}−\mathrm{1}\right)+\mathrm{4096}\right]\left(\mathrm{x}−\mathrm{1}\right)}\mathrm{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{thanks}!!! \\ $$ Answered by tanmay.chaudhury50@gmail.com…

find-arcsin-2x-1-4x-2-dx-

Question Number 45970 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:\int\:\:\frac{{arcsin}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by maxmathsup by imad last updated on 20/Oct/18 $${changement}\:{arcsin}\left(\mathrm{2}{x}\right)={t}\:\:{give}\:\:\mathrm{2}{x}={sint}\:\Rightarrow\mathrm{2}{dx}={cost}\:{dt}\:\Rightarrow…