Question Number 116996 by mnjuly1970 last updated on 08/Oct/20 Answered by mindispower last updated on 09/Oct/20 $${the}\:{last}\:{is}\:{li}_{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right)\int? \\ $$ Commented by mnjuly1970 last updated…
Question Number 51456 by Tawa1 last updated on 27/Dec/18 $$\int\:\:\:\frac{\mathrm{x}^{\mathrm{8}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{64}}\:\mathrm{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18 $${x}^{\mathrm{3}} =\mathrm{2}^{\mathrm{3}} {tan}\theta \\…
Question Number 182494 by universe last updated on 10/Dec/22 Commented by cortano1 last updated on 11/Dec/22 $$\left(\mathrm{c}\right)\:\pi \\ $$ Commented by mr W last updated…
Question Number 51421 by Tawa1 last updated on 26/Dec/18 $$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$ Commented by Tawa1 last updated on 27/Dec/18 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$ Commented…
Question Number 51419 by Tawa1 last updated on 26/Dec/18 $$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$ Answered by Smail last updated on 27/Dec/18 $${let}\:{u}=\sqrt[{\mathrm{6}}]{{x}}\Rightarrow\mathrm{6}{u}^{\mathrm{5}} {du}={dx} \\ $$$${A}=\int\frac{\sqrt{{x}}}{\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}}}{dx}=\int\frac{{u}^{\mathrm{3}} }{\mathrm{1}+{u}^{\mathrm{2}} }\left(\mathrm{6}{u}^{\mathrm{5}}…
Question Number 51394 by Tawa1 last updated on 26/Dec/18 $$\int\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\:\mathrm{dx} \\ $$ Answered by peter frank last updated on 26/Dec/18 Commented by Tawa1 last updated…
Question Number 116903 by mnjuly1970 last updated on 07/Oct/20 Answered by mathmax by abdo last updated on 07/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{acosx}\right)}{\mathrm{cosx}}\:\mathrm{dx}\:\:\left(\mathrm{here}\:\mathrm{a}=\mathrm{sin}\alpha\right)\:\Rightarrow \\ $$$$\mathrm{f}^{'} \left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi}…
Question Number 51353 by behi83417@gmail.com last updated on 26/Dec/18 Commented by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18 $$\left.\mathrm{1}\right){I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 51324 by Abdo msup. last updated on 25/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}\:} \:+{x}^{\mathrm{4}} } \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18 $$\int\frac{{dx}}{{x}^{\mathrm{4}}…
Question Number 116846 by mnjuly1970 last updated on 07/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\: \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{\frac{\left(\mathrm{2}^{{x}} −\mathrm{1}\right){sin}^{\mathrm{3}} \left({x}\right)}{\left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left({sin}^{\mathrm{3}} \left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)\right)}}\:\:{dx}<\frac{\pi}{\mathrm{8}}…