Question Number 117724 by bemath last updated on 13/Oct/20 $$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Commented by MJS_new last updated on 13/Oct/20 $$\mathrm{you}\:\mathrm{lost}\:\mathrm{the}\:“−''\:\mathrm{in}\:\mathrm{line}\:\mathrm{5} \\ $$$$\mathrm{btw}.:\:\mathrm{tan}\:\frac{\mathrm{arcsin}\:{x}}{\mathrm{2}}\:=\frac{{x}}{\mathrm{1}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}…
Question Number 183243 by cortano1 last updated on 24/Dec/22 $$\:\:\int\:\frac{\sqrt{\mathrm{sin}\:{x}}\:−\sqrt{\mathrm{cos}\:{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:+\:\sqrt{\mathrm{cos}\:{x}}}\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 24/Dec/22 $$\int\frac{\sqrt{\mathrm{sin}\:{x}}−\sqrt{\mathrm{cos}\:{x}}}{\:\sqrt{\mathrm{sin}\:{x}}+\sqrt{\mathrm{cos}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{t}}{{t}^{\mathrm{4}} +\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}\left({t}−\mathrm{1}\right)}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…
Question Number 52164 by pooja24 last updated on 04/Jan/19 $${find}: \\ $$$$\underset{\mathrm{0}} {\overset{\Pi} {\int}}\left({cos}^{\mathrm{6}} \theta\:−\mathrm{cos}\:^{\mathrm{4}} \theta\right)\:{d}\theta \\ $$$${plase}\:{help}\:{me}\:{in}\:{cinding}\:{this}\:{And}\:{also} \\ $$$${explain}\:{if}\:{possible} \\ $$ Commented by prakash…
Question Number 117654 by jeewanbee640 last updated on 13/Oct/20 Commented by prakash jain last updated on 13/Oct/20 $$\left({ii}\right)\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{period}\:\mathrm{2}\pi \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{2}\pi+\mathrm{1}\right)=\mathrm{8}\pi+\mathrm{4}\neq{f}\left(\mathrm{1}\right) \\ $$ Terms…
Question Number 117655 by jeewanbee640 last updated on 13/Oct/20 Commented by prakash jain last updated on 13/Oct/20 $${what}\:{is}\:{L}? \\ $$ Commented by bemath last updated…
Question Number 117638 by bemath last updated on 13/Oct/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{2x}^{\mathrm{12}} +\mathrm{5x}^{\mathrm{9}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=?\: \\ $$ Answered by john santu last updated…
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Question Number 183157 by cortano1 last updated on 21/Dec/22 $$\:\int\:\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{2019}}}\:=? \\ $$ Answered by MJS_new last updated on 21/Dec/22 $$\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{a}}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{{x}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +{a}}}\:\rightarrow\:{dx}=\frac{\sqrt[{\mathrm{3}}]{\left({x}^{\mathrm{3}}…
Question Number 183156 by cortano1 last updated on 21/Dec/22 $$\:\int\:\frac{\mathrm{sin}\:\mathrm{2}{x}\:{dx}}{\mathrm{sin}\:{x}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:=? \\ $$ Answered by MJS_new last updated on 21/Dec/22 $$\int\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{sin}\:{x}\:−\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{sin}\:{x}\:\rightarrow\:{dx}=\frac{{dt}}{\mathrm{cos}\:{x}}\right] \\…
Question Number 117574 by mnjuly1970 last updated on 12/Oct/20 $$\:\:\:\:\:\:\:\:…\:{advanced}\:\:{integral}… \\ $$$$\:\:\:\:\:\: \\ $$$$\mathscr{E}{valuate}\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{4}{xln}\left({x}\right)}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}\:}{dx}\:=??\: \\ $$$$\:\:\:\:\:…\:{m}.{n}.\mathrm{1970}.. \\ $$$$\: \\…