Question Number 196459 by RoseAli last updated on 25/Aug/23 Answered by Frix last updated on 25/Aug/23 $$\mathrm{Use}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\mathrm{to}\:\mathrm{get} \\ $$$$\int\frac{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx}=\frac{{x}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}}…
Question Number 196487 by RoseAli last updated on 25/Aug/23 $$\int\left(\mathrm{sec}\:^{\mathrm{4}} {x}−\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by MM42 last updated on 26/Aug/23 $${I}_{\mathrm{1}} =\int{sec}^{\mathrm{4}} {xdx}=\int\left(\mathrm{1}+{tan}^{\mathrm{2}} {x}\right)\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 196436 by RoseAli last updated on 24/Aug/23 $$\int\frac{{dx}}{{x}\left({x}^{{n}} −\mathrm{1}\right)} \\ $$ Answered by MM42 last updated on 24/Aug/23 $$\int\frac{{x}^{{n}} −\mathrm{1}+{x}^{{n}} }{{x}\left({x}^{{n}} −\mathrm{1}\right)}=\int\left(\frac{\mathrm{1}}{{x}}+\frac{{x}^{{n}−\mathrm{1}} }{{x}^{{n}}…
Question Number 196435 by RoseAli last updated on 24/Aug/23 Commented by Denis last updated on 24/Aug/23 Commented by RoseAli last updated on 24/Aug/23 $$\boldsymbol{\mathrm{thanks}} \\…
Question Number 196375 by RoseAli last updated on 23/Aug/23 $$\int\frac{{dx}}{{x}\left({x}^{\mathrm{4}} −\mathrm{1}\right)} \\ $$ Commented by RoseAli last updated on 23/Aug/23 $$\int\frac{{dx}}{{x}\left({x}^{\mathrm{4}} +\mathrm{1}\right)} \\ $$ Answered…
Question Number 196276 by SaRahAli last updated on 21/Aug/23 Answered by MM42 last updated on 21/Aug/23 $$\int\:\frac{{dx}}{\mathrm{1}+{sin}\mathrm{2}{x}}\:=\int\:\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}+{tanx}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\overset{\mathrm{1}+{tanx}={u}} {=}\:\int\:\frac{{du}}{{u}}\:={lnu}+{c} \\ $$$$={ln}\left(\mathrm{1}+{tanx}\right)+{c}\:\checkmark \\…
Question Number 196277 by cortano12 last updated on 21/Aug/23 $$\:\:\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$ Answered by mr W last updated on 21/Aug/23 $${say}\:{z}=\mathrm{sin}^{\mathrm{3}} \:{x} \\ $$$$\frac{{dz}}{{dy}}=\frac{{dz}}{{dx}}×\frac{{dx}}{{dy}}=\mathrm{3}\:\mathrm{sin}^{\mathrm{2}}…
Question Number 196173 by pticantor last updated on 19/Aug/23 $$\boldsymbol{{Calcul}}\:\boldsymbol{{I}}_{\boldsymbol{{a}}} =\int_{\boldsymbol{{a}}} ^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} \frac{\boldsymbol{{lnx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:\left(\boldsymbol{{a}}>\mathrm{0}\right)\: \\ $$ Answered by Erico last updated on 19/Aug/23 $$\:\mathrm{J}_{{a}} =\:\underset{\:\mathrm{1}}…
Question Number 196046 by arkanshh last updated on 17/Aug/23 $$\int{e}^{{x}^{\mathrm{2}} } \:{ln}^{\mathrm{24}} \left({x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196037 by cortano12 last updated on 16/Aug/23 $$\:\:\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 16/Aug/23 $$\mathrm{Use}\:{t}=\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{4}}\right)\:\Rightarrow\:{dx}=\frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:\mathrm{to}\:\mathrm{get} \\ $$$$\sqrt{\mathrm{2}}\int\frac{\mathrm{2}{t}^{\mathrm{2}}…