Question Number 200299 by Calculusboy last updated on 16/Nov/23 Answered by witcher3 last updated on 17/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\Omega=\int_{\infty} ^{\mathrm{0}} −\frac{\frac{\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{x}}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} }.\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}}…
Question Number 200256 by Calculusboy last updated on 16/Nov/23 Commented by Rasheed.Sindhi last updated on 17/Nov/23 $${In}\:{first}\:{sight}\:{your}\:{post}\:{seems} \\ $$$$\left.{to}\:{be}\:{red}\:{flagged}!\::\right) \\ $$ Terms of Service Privacy…
Question Number 200257 by Calculusboy last updated on 16/Nov/23 Answered by witcher3 last updated on 16/Nov/23 $$\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{1}=\mathrm{y}\Rightarrow\mathrm{dy}=\mathrm{2}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}} \\ $$$$=\int\mathrm{y}^{\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{y}\right)\mathrm{dy} \\ $$$$=\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{3}}\mathrm{tan}^{−\mathrm{1}}…
Question Number 200159 by Calculusboy last updated on 15/Nov/23 Commented by 0670322918 last updated on 15/Nov/23 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \frac{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}}{dx}= \\…
Question Number 200155 by Calculusboy last updated on 15/Nov/23 Answered by Frix last updated on 15/Nov/23 $${s}>\mathrm{0} \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\sqrt{{t}}\mathrm{e}^{−{st}} {dt}= \\ $$$$=−\frac{\mathrm{1}}{{s}}\left[\sqrt{{t}}\mathrm{e}^{−{st}} \right]_{\mathrm{0}}…
Question Number 200130 by universe last updated on 14/Nov/23 $$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$ Answered by Mathspace last updated on 14/Nov/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 200061 by universe last updated on 13/Nov/23 $$\:\:\:\:\int_{−\infty} ^{+\infty} \frac{{x}\mathrm{sin}{x}\:}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:=\:\:\:?? \\ $$ Answered by witcher3 last updated on 13/Nov/23 $$\int_{−\infty} ^{\infty}…
Question Number 200048 by Calculusboy last updated on 12/Nov/23 Commented by 0670322918 last updated on 13/Nov/23 $$\int\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\int{tan}^{−\mathrm{1}} \left({x}\right){dx}}{dx}= \\ $$$${f}\left({x}\right)=\int{tan}^{−\mathrm{1}} \left({x}\right){dx}={xtan}^{−\mathrm{1}} \left({x}\right)−\frac{\mathrm{1}}{\mathrm{2}}{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)+{c} \\…
Question Number 199934 by cortano12 last updated on 11/Nov/23 $$\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$$$ \\ $$ Answered by mr W last updated on 11/Nov/23 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 199921 by Mingma last updated on 11/Nov/23 Answered by des_ last updated on 12/Nov/23 $$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\:{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:{I}; \\ $$$${I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx},\:{a}\:>\mathrm{0};…