Category: Integration

Question Number 84379 by Power last updated on 12/Mar/20 Answered by mind is power last updated on 12/Mar/20 $$=\int\frac{{x}\mathrm{2}{i}}{{e}^{{ix}} −{e}^{−{ix}} }{dx} \\ $$$$=\int\frac{{x}\mathrm{2}{ie}^{{ix}} }{\left({e}^{\mathrm{2}{ix}} −\mathrm{1}\right)}{dx}={f}\left({x}\right)…

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 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}}…

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 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}}…