Question Number 48955 by Abdulhafeez Abu qatada last updated on 30/Nov/18 $${Evaluate}\:\underset{\mathrm{0}} {\overset{\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}} {\int}}\:\frac{\mathrm{2}{x}\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 30/Nov/18…
Question Number 114472 by mnjuly1970 last updated on 19/Sep/20 $$\:\:\:\:\:\:\:\:\:…\:\:{calculus}… \\ $$$${evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{cos}^{\mathrm{2}} \left({x}\right)}−\sqrt{{cos}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{sin}^{\mathrm{2}} \left({x}\right)\:}}\:{dx}=\:??? \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}…. \\…
Question Number 114467 by Eric002 last updated on 19/Sep/20 $$\int{x}\:{sin}^{{n}} \left({x}\right)\:{dx} \\ $$ Answered by Olaf last updated on 19/Sep/20 $$\mathrm{I}_{{n}} \left({x}\right)\:=\:\int{x}\mathrm{sin}^{{n}} {xdx} \\ $$$$\mathrm{I}_{{n}}…
Question Number 179991 by mnjuly1970 last updated on 05/Nov/22 Answered by mindispower last updated on 05/Nov/22 $$=\underset{{n}\geqslant\mathrm{2}} {\sum}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{m}!}{x}^{{m}} {e}^{−{nx}} {dx}=\frac{\mathrm{1}}{{m}!}\int_{\mathrm{0}} ^{\infty} \left(\frac{{y}}{{n}}\right)^{{m}} {e}^{−{y}}…
Question Number 114403 by bemath last updated on 19/Sep/20 $$\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{4}} \right)}{{x}}\:{dx} \\ $$$$ \\ $$ Commented by Dwaipayan Shikari last updated on 19/Sep/20 $$\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 114395 by mathmax by abdo last updated on 18/Sep/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{x}}\mathrm{dx} \\ $$ Answered by Olaf last updated on 19/Sep/20…
Question Number 48829 by Ali Yousafzai last updated on 29/Nov/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int\mathrm{1}^{{x}} \left[{t}^{\mathrm{2}} \left({e}^{\mathrm{1}/{t}} −\mathrm{1}\right)−{t}\right]{dt}}{{x}^{\mathrm{2}} \mathrm{ln}\:\left(\mathrm{1}+\mathrm{1}/{x}\right)} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 114330 by mnjuly1970 last updated on 18/Sep/20 Commented by mnjuly1970 last updated on 18/Sep/20 $${easy}\:{question}\uparrow\uparrow\uparrow \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 179862 by cherokeesay last updated on 03/Nov/22 Commented by CElcedricjunior last updated on 03/Nov/22 $$\begin{cases}{\boldsymbol{{y}}=\boldsymbol{{lnx}}}\\{\boldsymbol{{y}}=\mathrm{2}}\end{cases}=>\boldsymbol{{lnx}}=\mathrm{2}=>\boldsymbol{{x}}=\boldsymbol{{e}}^{\mathrm{2}} \\ $$$$\left.=\left.>\boldsymbol{{x}}\in\right]\mathrm{0};\boldsymbol{{e}}^{\mathrm{2}} \right]\:\boldsymbol{{et}}\:\boldsymbol{{y}}\in\left[\boldsymbol{{lnx}};\mathrm{2}\right] \\ $$$$\Leftrightarrow\boldsymbol{{A}}=\int_{\boldsymbol{{lnx}}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\boldsymbol{{e}}^{\mathrm{2}}…
Question Number 179853 by AKSHAYTHAKUR last updated on 03/Nov/22 $$\int\frac{\boldsymbol{{xdx}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)} \\ $$ Commented by CElcedricjunior last updated on 04/Nov/22 $$\int\:\frac{\boldsymbol{{xdx}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)}=\int\left[\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{2}}+\frac{\mathrm{1}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)}\right]\boldsymbol{{dx}} \\ $$$$={ln}\mid\boldsymbol{{x}}−\mathrm{2}\mid+\int\left[−\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{1}}+\frac{\mathrm{1}}{\boldsymbol{{x}}−\mathrm{2}}\right]\boldsymbol{{dx}} \\ $$$$=\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{2}\mid−\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{1}\mid+\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{1}\mid \\…