Question Number 41561 by Tawa1 last updated on 09/Aug/18 $$\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\left(\mathrm{x}\right)\:+\:\mathrm{4cos}\left(\mathrm{x}\right)} \\ $$ Commented by math khazana by abdo last updated on 09/Aug/18 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}\:\:=\:\int\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{3}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 172635 by Mikenice last updated on 29/Jun/22 Answered by MJS_new last updated on 29/Jun/22 $$\int\frac{\mathrm{4}^{{x}} }{\mathrm{4}^{{x}} +\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{4}^{{x}} +\mathrm{1}\:\rightarrow\:{dx}=\frac{{dt}}{\mathrm{4}^{{x}} \:\mathrm{ln}\:\mathrm{4}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{4}}\int\frac{{dt}}{{t}}=\frac{\mathrm{ln}\:{t}}{\mathrm{ln}\:\mathrm{4}}=…
Question Number 41555 by Raj Singh last updated on 09/Aug/18 Answered by alex041103 last updated on 09/Aug/18 $$\mathrm{1}.\:\int\frac{{ln}\:{x}}{\left(\mathrm{1}+{ln}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$$${let}\:{x}={e}^{{u}} \:{dx}={e}^{{u}} {du}. \\ $$$$\int\frac{\mathrm{1}+{u}−\mathrm{1}}{\left(\mathrm{1}+{u}\right)^{\mathrm{2}}…
Question Number 172606 by Mikenice last updated on 29/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 172607 by Mikenice last updated on 29/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 172600 by Mikenice last updated on 29/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 172602 by Mikenice last updated on 29/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 41518 by maxmathsup by imad last updated on 08/Aug/18 $${calculate}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{{n}} {dt}\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$ Answered by alex041103 last updated on…
Question Number 41516 by maxmathsup by imad last updated on 08/Aug/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{4}} }\:{dx} \\ $$ Commented by turbo msup by abdo last updated…
Question Number 41515 by maxmathsup by imad last updated on 08/Aug/18 $$\left.{l}\left.{et}\:\:{f}_{{n}} \left({x}\right)\:=\frac{{sin}\left(\mathrm{2}\left({n}+\mathrm{1}\right){x}\right)}{{sinx}}\:{if}\:\:{x}\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\right]\:{and}\:{f}_{{n}} \left(\mathrm{0}\right)=\mathrm{2}\left({n}+\mathrm{1}\right)\:\:{let} \\ $$$${u}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{f}_{{n}} \left({x}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\forall{n}\:{fromN}\:\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} =\mathrm{2}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{3}}…