Question Number 176289 by infinityaction last updated on 15/Sep/22 $$\:\:\int\:\:\frac{\mathrm{log}\:\left(\mathrm{cos}{x}\:+\:\sqrt{\mathrm{cos2}{x}}\right)\:}{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\:}{dx} \\ $$ Commented by infinityaction last updated on 16/Sep/22 $$\int\boldsymbol{\mathrm{cosec}}^{\mathrm{2}} \boldsymbol{{x}}\:\boldsymbol{\mathrm{log}}\left[\boldsymbol{\mathrm{sin}{x}}\left(\boldsymbol{\mathrm{cotx}}\:+\:\sqrt{\boldsymbol{\mathrm{cot}}^{\mathrm{2}} \boldsymbol{{x}}−\mathrm{1}\:}\right)\boldsymbol{\mathrm{dx}}\right. \\ $$$$\underset{\Psi_{\mathrm{1}}…
Question Number 110749 by mnjuly1970 last updated on 30/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:{please}\:{evaluate}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}}\:{dx}=???\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.\mathscr{J}{uly}\:\mathrm{1970}# \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:\mathscr{G}{ood}\:\:{luck}…. \\ $$$$…
Question Number 45201 by maxmathsup by imad last updated on 10/Oct/18 $${find}\:\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }} \\ $$ Commented by Meritguide1234 last updated on 10/Oct/18 Commented by MJS…
Question Number 45164 by Tinkutara last updated on 09/Oct/18 Commented by maxmathsup by imad last updated on 09/Oct/18 $${let}\:\varphi\left({x}\right)=\:\left(\frac{{x}+{a}}{{x}+{b}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:=\left(\frac{{x}+{b}\:+{a}−{b}}{{x}+{b}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:=\left(\mathrm{1}+\frac{{a}−{b}}{{x}+{b}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:\Rightarrow \\ $$$$\varphi^{'} \left({x}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(−\frac{{a}−{b}}{\left({x}+{b}\right)^{\mathrm{2}}…
Question Number 45165 by Tinkutara last updated on 09/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Oct/18 $$\int\frac{{sin}\mathrm{5}{x}\left(\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}.{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}{{sin}\mathrm{5}{x}−{sin}\mathrm{10}{x}}{dx} \\ $$$$\int\frac{\mathrm{2}{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}{cos}\frac{\mathrm{5}{x}}{\mathrm{2}}\left(\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}{−\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}.{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{dx} \\ $$$$=−\int\mathrm{2}{cos}\frac{\mathrm{5}{x}}{\mathrm{2}}.{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}{dx} \\ $$$$=−\int{cos}\mathrm{4}{x}+{cosx}\:\:\:{dx} \\ $$$$=−\left(\frac{{sin}\mathrm{4}{x}}{\mathrm{4}}+{sinx}\right)+{c}…
Question Number 45155 by rahul 19 last updated on 09/Oct/18 Commented by rahul 19 last updated on 09/Oct/18 $${It}'{s}\:{a}\:{very}\:{beautiful}\:{Ques}…. \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 45158 by rahul 19 last updated on 09/Oct/18 $$\:\:\int\frac{{e}^{\mathrm{2}{x}} −{e}^{{x}} +\mathrm{1}}{\left({e}^{{x}} {sinx}+{cosx}\right)\left({e}^{{x}} {cosx}−{sinx}\right)}{dx}\:=? \\ $$ Commented by Meritguide1234 last updated on 10/Oct/18 Terms…
Question Number 45151 by Tinkutara last updated on 09/Oct/18 Commented by Meritguide1234 last updated on 10/Oct/18 Commented by Tinkutara last updated on 10/Oct/18 Thank you very much Sir! I got the answer. �������� Terms…
Question Number 45128 by Necxx last updated on 09/Oct/18 Commented by Necxx last updated on 09/Oct/18 $${please}\:{help}\:{with}\:{the}\:{last}\:{question}_{} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 45117 by rahul 19 last updated on 09/Oct/18 $${Prove}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{a}} −\mathrm{1}}{\mathrm{log}\:{x}}\:{dx}\:=\:\mathrm{log}\:\left({a}+\mathrm{1}\right). \\ $$ Commented by maxmathsup by imad last updated on 09/Oct/18…