Question Number 216408 by MrGaster last updated on 07/Feb/25 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\mathrm{ln}\left(\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}\right){dx} \\ $$ Commented by MrGaster last updated on 07/Feb/25 $${I}=\int_{−\mathrm{1}} ^{+\mathrm{1}}…
Question Number 216381 by glory86 last updated on 06/Feb/25 $$\int\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$ Answered by mr W last updated on 06/Feb/25 $$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} {dx} \\ $$$$={x}\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}}…
Question Number 216372 by glory86 last updated on 06/Feb/25 $$\int\frac{{xe}^{{x}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by MrGaster last updated on 06/Feb/25 $$\mathrm{Let}\:{u}={x}+\mathrm{1}\Rightarrow{du}={dx},{x}={u}−\mathrm{1} \\ $$$$\int\frac{\left({u}−\mathrm{1}\right){e}^{{u}−\mathrm{1}} }{{u}^{\mathrm{2}}…
Question Number 216390 by jucimar last updated on 06/Feb/25 $${f}\left({x}\right)={ax}\: \\ $$ Commented by issac last updated on 07/Feb/25 $${f}\left({x}\right)={ax}….??\: \\ $$ Commented by MrGaster…
Question Number 216296 by MrGaster last updated on 03/Feb/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 216281 by MrGaster last updated on 02/Feb/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {d}\phi\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\theta\:\mathrm{cos}\:\theta\right)\mathrm{sin}\theta\:{d}\theta=\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$ Commented by mr W last updated on…
Question Number 216093 by mnjuly1970 last updated on 27/Jan/25 Answered by mahdipoor last updated on 27/Jan/25 $${note}\::\:\mathrm{0}\leqslant{x}<\mathrm{1}\:\:,\:\:{y}^{\mathrm{2}} =\left(\mathrm{1}+{y}^{\mathrm{2}} \right){x} \\ $$$${get}\:\:{f}={ln}\left({y}\right)+{ln}\left({y}'\right) \\ $$$$\Rightarrow\frac{{df}}{{dx}}=\frac{{y}^{'} }{{y}}+\frac{{y}^{''} }{{y}'}=\mathrm{2}\varphi…
Question Number 216042 by ajfour last updated on 26/Jan/25 $$\left({i}\right)\:\:\:\int\mathrm{sec}\:^{\mathrm{5}} \theta{d}\theta \\ $$$$\left({ii}\right)\:\:\int\:\frac{\sqrt{\mathrm{tan}\:\theta}\:{d}\theta}{\mathrm{cos}\:\theta} \\ $$ Commented by ajfour last updated on 26/Jan/25 https://youtu.be/VqEdd_VGxGI?si=VnVRn7bW5wENyi9Y Find radius of circle inscribed in half ellipse. Commented by…
Question Number 215995 by universe last updated on 25/Jan/25 $$\int\int\underset{{D}} {\int}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }\:\mathrm{dv}\:=\:? \\ $$$$\mathrm{D}\:=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} <{z} \\ $$ Answered by mr W…
Question Number 215963 by RoseAli last updated on 23/Jan/25 Answered by Frix last updated on 23/Jan/25 $$\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} \left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:{x}\right){dx}= \\ $$$$=\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} \left(\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{cos}^{\mathrm{2}} \:{x}\right){dx}= \\…