Question Number 149885 by puissant last updated on 08/Aug/21 $${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{dx}}{{cos}^{\mathrm{2}{n}+\mathrm{1}} {x}} \\ $$$${to}\:{show}\:{that}\:: \\ $$$$\forall\:{n}\in\mathbb{N}^{\ast} ,\:\mathrm{2}{nI}_{{n}} =\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} +\frac{\mathrm{2}^{{n}} }{\:\sqrt{\mathrm{2}}} \\ $$$$\left({I}_{{n}} =\int_{\mathrm{0}}…
Question Number 84334 by sahnaz last updated on 11/Mar/20 $$\int\frac{\mathrm{1}−\mathrm{u}}{−\mathrm{1}−\mathrm{2u}+\mathrm{u}^{\mathrm{2}} }\mathrm{du} \\ $$ Commented by niroj last updated on 11/Mar/20 $$\:\:\int\:\frac{−\left(\mathrm{u}−\mathrm{1}\right)}{−\left(\mathrm{1}+\mathrm{2u}−\mathrm{u}^{\mathrm{2}} \right)}\mathrm{du} \\ $$$$\:\:\:\int\:\frac{{u}−\mathrm{1}}{\mathrm{1}+\mathrm{2}{u}−{u}^{\mathrm{2}} }{du}…
Question Number 84313 by M±th+et£s last updated on 11/Mar/20 $$\int\:\:\left({a}^{\mathrm{2}/\mathrm{5}} −{x}^{\mathrm{2}/\mathrm{5}} \right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:{dx} \\ $$ Commented by niroj last updated on 11/Mar/20 $$\:\int\:\left(\mathrm{a}^{\mathrm{2}/\mathrm{5}} −\mathrm{x}^{\mathrm{2}/\mathrm{5}} \right)^{\mathrm{5}/\mathrm{2}}…
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Question Number 84246 by pew_247 last updated on 10/Mar/20 $$\int\mathrm{cos}^{{n}} \:{mx}\:\:{dx}\:= \\ $$ Answered by TANMAY PANACEA last updated on 10/Mar/20 $${I}_{{n},{m}} =\int{cos}^{{n}} {mxdx}=\int{cos}^{{n}−\mathrm{1}} {mx}.{cosmxdx}…
Question Number 149772 by Samimsultani last updated on 07/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149773 by Samimsultani last updated on 07/Aug/21 Answered by puissant last updated on 07/Aug/21 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{b}^{\mathrm{2}} }{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}}…
Question Number 84234 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}: \\ $$$$\:\:\:\mathrm{1}.\:\int\sqrt{\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\mathrm{2}.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\left(\mathrm{3}+\mathrm{2}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)} \\ $$$$\: \\ $$ Commented by mathmax by abdo last updated…
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Question Number 149739 by iloveisrael last updated on 07/Aug/21 Answered by Olaf_Thorendsen last updated on 07/Aug/21 $$\lambda\:=\:\int_{\mathrm{0}} ^{\pi} {x}\mathrm{sin}^{\mathrm{9}} {x}\:{dx}\:\:\:\left(\mathrm{1}\right) \\ $$$$\lambda\:=\:\int_{\pi} ^{\mathrm{0}} \left(\pi−{u}\right)\mathrm{sin}^{\mathrm{9}} \left(\pi−{u}\right)\:\left(−{du}\right)…