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Question Number 153721 by mnjuly1970 last updated on 09/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}^{\:\mathrm{3}} }{{sinh}\:\left(\:{x}\:\right)}\:{dx}\:=\:\frac{\pi\:^{\mathrm{4}} }{\mathrm{8}}\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…
Question Number 88181 by ubaydulla last updated on 08/Apr/20 Commented by mathmax by abdo last updated on 09/Apr/20 $$\left.\mathrm{5}\right)\:{y}^{'} \:+{y}\:={e}^{\mathrm{2}{x}} \:\:\:\left({he}\right)\rightarrow{y}^{'} \:+{y}\:=\mathrm{0}\Rightarrow\frac{{y}^{'} }{{y}}=−\mathrm{1}\:\Rightarrow{ln}\mid{y}\mid=−{x}\:+{c}\:\Rightarrow \\ $$$${y}\:={k}\:{e}^{−{x}}…
Question Number 88177 by M±th+et£s last updated on 08/Apr/20 $${prove}\:{that} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2020}} \left({x}−\left[{x}\right]\right)\sqrt{{x}−\left[{x}\right]}\:{dx}=\mathrm{808} \\ $$ Answered by TANMAY PANACEA. last updated on…
Question Number 88170 by Ar Brandon last updated on 08/Apr/20 $${Prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tcos}\:{n}\pi{tdt}=\frac{\left(−\mathrm{1}\right)^{{n}} −\mathrm{1}}{{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$ Commented by jagoll last updated…
Question Number 22621 by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{x}\right)^{\mathrm{n}} }\left(\mathrm{n}\neq\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{z}^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{z}^{\mathrm{n}−\mathrm{1}} }{\mathrm{n}−\mathrm{1}}\right)+\mathrm{cccccc} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\mathrm{z}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 22623 by tawa tawa last updated on 21/Oct/17 $$\mathrm{How}\:\mathrm{is}:\:\:\:\int\:\frac{\mathrm{x}\:+\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\mathrm{xtan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:+\:\mathrm{C} \\ $$ Answered by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{x}+\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}\mathrm{dx}\:\: \\ $$$$\int\frac{\mathrm{x}}{\mathrm{2cos}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}+\frac{\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 88153 by Chi Mes Try last updated on 08/Apr/20 Commented by Prithwish Sen 1 last updated on 08/Apr/20 $$\mathrm{sin}^{−\mathrm{1}} \mathrm{e}^{\mathrm{x}} \:+\:\mathrm{sec}^{−\mathrm{1}} \left(\mathrm{e}^{−\mathrm{x}} \right)\:=\:\mathrm{sin}^{−\mathrm{1}}…
Question Number 88131 by M±th+et£s last updated on 08/Apr/20 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx} \\ $$ Answered by MJS last updated on 08/Apr/20 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{1}−\mathrm{2}{x}}\:\rightarrow\:{dx}−\sqrt{\mathrm{1}−\mathrm{2}{x}}{dt}\right] \\…
Question Number 88118 by sahnaz last updated on 08/Apr/20 $$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)×\sqrt{\mathrm{x}}} \\ $$ Commented by mathmax by abdo last updated on 08/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}}}\:\Rightarrow{I}\:=_{{x}={t}^{\mathrm{2}} } \:\:\int\:\:\:\frac{\mathrm{2}{tdt}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right){t}}\:=\mathrm{2}\:\int\:\:\frac{{dt}}{{t}^{\mathrm{2}}…