Question Number 17475 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{e}} ^{\mathrm{e}^{\mathrm{2}} } \frac{\mathrm{ln}{x}}{\left(\mathrm{1}+\mathrm{ln}{x}\right)^{\mathrm{2}} }\mathrm{d}{x}=\frac{\mathrm{e}}{\mathrm{6}}\left(\mathrm{2e}−\mathrm{3}\right) \\ $$ Answered by ajfour last updated on 06/Jul/17 $$\mathrm{lnx}=\mathrm{t}\:\:\:\Rightarrow\:\:\:\frac{\mathrm{dx}}{\mathrm{x}}=\mathrm{dt}\:\:\mathrm{or}\:\:\mathrm{dx}=\mathrm{e}^{\mathrm{t}}…
Question Number 83009 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({chx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 17472 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{6}} ^{\mathrm{11}} \frac{\mathrm{dx}}{\:\sqrt{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}−\mathrm{3}\right)}}=\mathrm{2ln}\frac{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}} \\ $$ Answered by sma3l2996 last updated on 06/Jul/17 $${I}=\int_{\mathrm{6}} ^{\mathrm{11}} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 17463 by alex041103 last updated on 06/Jul/17 $${Evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}. \\ $$ Answered by ajfour last updated on 06/Jul/17 $$\frac{\mathrm{22}}{\mathrm{7}}−\pi\:.…
Question Number 17444 by Tinkutara last updated on 06/Jul/17 $$\mathrm{Evaluate}:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\mathrm{cos}^{\mathrm{3}} \:{x}\:\sqrt{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}}} \\ $$ Answered by Arnab Maiti last updated on 10/Jul/17 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 82974 by Power last updated on 26/Feb/20 Commented by Power last updated on 27/Feb/20 $$\mathrm{sir}\:\mathrm{mind}\:\mathrm{is}\:\mathrm{power}\:\:\mathrm{pls} \\ $$ Answered by mind is power last…
Question Number 82972 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82970 by mathmax by abdo last updated on 26/Feb/20 $$\left.\mathrm{1}\right){find}\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$ Commented by mathmax…
Question Number 82971 by mathmax by abdo last updated on 26/Feb/20 $$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$ Commented by mathmax…
Question Number 82954 by john santu last updated on 26/Feb/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$ Commented by john santu last updated on 26/Feb/20 $$\mathrm{let}\:\mathrm{u}=\:\mathrm{cos}\:\mathrm{2x}\:\Rightarrow\:\mathrm{dx}\:=\:−\frac{\mathrm{du}}{\mathrm{2}\sqrt{\mathrm{1}−\mathrm{u}^{\mathrm{2}} }} \\ $$$$\Rightarrow\int\:\frac{\:\mathrm{2u}^{\mathrm{2}}…