Question Number 25183 by ajfour last updated on 06/Dec/17 $${Prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\:\infty} \frac{{x}^{\mathrm{6}} {dx}}{\left({a}^{\mathrm{4}} +{x}^{\mathrm{4}} \right)^{\mathrm{2}} }=\:\frac{\mathrm{3}\pi\sqrt{\mathrm{2}}}{\mathrm{16}{a}}\:\:\:,\:\:\left({a}>\mathrm{0}\right)\:. \\ $$ Commented by prakash jain last…
Question Number 90717 by ~blr237~ last updated on 25/Apr/20 $${Prove}\:{that}\:{for}\:{all}\:{integer}\:{r}\geqslant\mathrm{2}\: \\ $$$$\:{HCF}\left({r}^{{n}} −\mathrm{1};{r}^{{m}} −\mathrm{1}\right)={r}^{{HCF}\left({n};{m}\right)} −\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156228 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{log}^{\mathrm{3}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{3}} }\:{dx} \\ $$$$\: \\ $$ Answered by smallEinstein last…
Question Number 156229 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{2}{x}\right)+\mathrm{cos}\left(\mathrm{3}{x}\right)\right)\:{dx} \\ $$$$\: \\ $$ Commented by talminator2856791 last updated on 09/Oct/21…
Question Number 156222 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}\left(\left(\mathrm{sin}\left({x}\right)\mathrm{cos}\left({x}\right)\right)^{\mathrm{2}} +\mathrm{1}\right)\:{dx} \\ $$$$\: \\ $$ Commented by talminator2856791 last updated on…
Question Number 156224 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}^{\mathrm{2}} \right)+\mathrm{1}}\:}\:{dx} \\ $$$$\: \\ $$ Commented by talminator2856791 last updated on…
Question Number 156218 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}}}\:}\:{dx} \\ $$$$\: \\ $$ Commented by talminator2856791 last…
Question Number 156194 by talminator2856791 last updated on 09/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} …..\sqrt{{x}^{{n}} }}}}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{n}\:\in\:\mathbb{N} \\ $$$$\: \\ $$ Commented by…
Question Number 156177 by amin96 last updated on 08/Oct/21 $$\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=? \\ $$ Answered by mathmax by abdo last updated on 10/Oct/21 $$\Psi=\int_{−\infty}…
Question Number 156182 by cortano last updated on 09/Oct/21 Answered by PRITHWISH SEN 2 last updated on 10/Oct/21 $$\int\frac{\mathrm{sec}^{\mathrm{4}} \mathrm{xdx}}{\mathrm{12tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4}}\:=\:\int\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx}}{\mathrm{12tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4}} \\…