Question Number 167024 by peter frank last updated on 04/Mar/22 $$\int\mathrm{sec}\:\theta\mathrm{tan}\:^{\mathrm{4}} \theta\mathrm{d}\theta \\ $$ Answered by cortano1 last updated on 05/Mar/22 $$\:\mathrm{let}\:\mathrm{t}\:=\:\mathrm{tan}\:\theta \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{t}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
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Question Number 35949 by ajfour last updated on 26/May/18 $$\int_{\mathrm{0}} ^{\:\:\alpha} \frac{\mathrm{tan}\:\theta}{\:\sqrt{{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta−{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta}}\:{d}\theta\:=\:? \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 167006 by cortano1 last updated on 04/Mar/22 $$\:\:\:\:\:\:\:\int\:\frac{\mathrm{3x}^{\mathrm{3}} }{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}=? \\ $$ Answered by MJS_new last updated on 04/Mar/22 $$\int\frac{\mathrm{3}{x}^{\mathrm{3}} }{\left({x}−\mathrm{1}\right)^{\mathrm{3}} }{dx}=\int\frac{\mathrm{3}\left({t}+\mathrm{1}\right)^{\mathrm{3}} }{{t}^{\mathrm{3}}…
Question Number 101461 by Dwaipayan Shikari last updated on 02/Jul/20 Answered by MAB last updated on 02/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\:\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} }=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\frac{{r}}{{n}}}\left(\mathrm{3}\sqrt{\frac{{r}}{{n}}}+\mathrm{4}\right)^{\mathrm{2}}…
Question Number 35920 by rahul 19 last updated on 25/May/18 $$\int\:\frac{{e}^{\mathrm{2}{x}} +\mathrm{1}}{\mathrm{2}{e}^{{x}} −\mathrm{1}}\:{dx}\:=\:? \\ $$ Commented by prof Abdo imad last updated on 26/May/18 $${changement}\:{e}^{{x}}…
Question Number 101451 by yahyajan last updated on 02/Jul/20 Commented by Dwaipayan Shikari last updated on 02/Jul/20 $${sin}^{−\mathrm{1}} {x}\int\mathrm{1}{dx}−\int\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$${xsin}^{−\mathrm{1}} {x}\:+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}\:\:\:={xsin}^{−\mathrm{1}} {x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 35909 by ajfour last updated on 25/May/18 $$\int\frac{\mathrm{7}{x}−\mathrm{6}}{\left({x}^{\mathrm{2}} +\mathrm{25}\right)\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:=\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 26/May/18 $${this}\:{nut}\:{is}\:{hard}\:{to}\:{crack}…{i}\:{am}\:{fighting}..{hope} \\ $$$${reach}\:{the}\:{destination}\:{to}\:{get}\:{it}\:{solved}… \\…
Question Number 166956 by mnjuly1970 last updated on 03/Mar/22 $$ \\ $$$$\:\:\:\:{calculate} \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}\:{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\:\mathrm{2}} }{dx}\:=? \\ $$ Answered by ArielVyny last updated on…
Question Number 166959 by cortano1 last updated on 03/Mar/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\gamma=\int\:\frac{\mathrm{e}^{\mathrm{x}} \left(\mathrm{sin}\:\mathrm{x}+\mathrm{1}\right)}{\mathrm{cos}\:\mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Answered by ArielVyny last updated on 03/Mar/22 $$\gamma=\int\frac{{e}^{{x}} \left({sinx}+\mathrm{1}\right)}{{cosx}+\mathrm{1}}{dx} \\ $$$${t}={tan}\left(\frac{{x}}{\mathrm{2}}\right)\rightarrow\mathrm{2}{arctan}\left({t}\right)={x} \\…