Question Number 83085 by mathmax by abdo last updated on 27/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Commented by abdomathmax…
Question Number 83064 by M±th+et£s last updated on 27/Feb/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}\left({nx}\right)}{{sin}\left({x}\right)}{dx}=\frac{\pi}{\mathrm{2}} \\ $$$${n}\:{is}\:{posative}\:{odd}\:{number} \\ $$ Answered by mind is power last updated…
Question Number 83063 by M±th+et£s last updated on 27/Feb/20 Commented by M±th+et£s last updated on 27/Feb/20 $${thank}\:{you}\:{sir} \\ $$ Commented by abdomathmax last updated on…
Question Number 17525 by alex041103 last updated on 07/Jul/17 $$\mathrm{Evaluate}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\frac{{n}}{\mathrm{2}}} {dx}\:\:\mathrm{for}\: \\ $$$${n}\:\in\:\mathbb{Z}\cap\left[\mathrm{0};\infty\right)\:\left(\mathrm{i}.\mathrm{e}.\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right)\:\mathrm{and}: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\:{n}\:\equiv\:\mathrm{0}\left({mod}\:\mathrm{2}\right) \\ $$$$\left.\boldsymbol{{b}}\right)\:{n}\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{2}\right) \\ $$ Commented by alex041103…
Question Number 17522 by sayan last updated on 07/Jul/17 $$\int\frac{{dx}}{\mathrm{sin}\:^{\mathrm{5}} {x}+\mathrm{cos}\:^{\mathrm{5}} {x}} \\ $$ Commented by 1kanika# last updated on 07/Jul/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answere}\:. \\ $$ Terms…
Question Number 17514 by sma3l2996 last updated on 07/Jul/17 $${S}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}{n}} {sin}\left(\mathrm{2}{n}\pi{x}\right){dx} \\ $$ Commented by alex041103 last updated on 07/Jul/17 $$\mathrm{Is}\:{n}\:\mathrm{a}\:\mathrm{whole}\:\mathrm{number}? \\ $$…
Question Number 17512 by tawa tawa last updated on 06/Jul/17 $$\int\:\frac{\mathrm{e}^{−\mathrm{t}} \:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{e}^{−\mathrm{t}} \right)}{\mathrm{1}\:+\:\mathrm{e}^{−\mathrm{t}} }\:\mathrm{dt} \\ $$ Answered by sma3l2996 last updated on 07/Jul/17 $${I}=\int\frac{{e}^{−{t}} {ln}\left(\mathrm{1}+{e}^{−{t}}…
Question Number 17506 by tawa tawa last updated on 06/Jul/17 $$\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{1}}}\right)\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 06/Jul/17 $${u}={tan}^{−\mathrm{1}} \left(\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}\right)\Rightarrow{u}'=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}}=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}} \\…
Question Number 148565 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)} \\ $$ Answered by Ar Brandon last updated…
Question Number 148570 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 29/Jul/21…