Question Number 49939 by turbo msup by abdo last updated on 12/Dec/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sinx}\:{ln}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 12/Dec/18 Commented…
Question Number 115464 by bemath last updated on 26/Sep/20 $${I}=\:\underset{\mathrm{0}\:} {\overset{\mathrm{1}} {\int}}\:{x}\:\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:{dx}\:? \\ $$$${I}=\int\:\sqrt{\mathrm{sin}\:{x}}\:.\mathrm{cos}\:^{\mathrm{3}} {x}\:{dx}\:? \\ $$ Answered by malwaan last updated on 26/Sep/20…
Question Number 49922 by Pk1167156@gmail.com last updated on 12/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 12/Dec/18 $$\int\frac{{x}^{\mathrm{4}} {dx}}{{x}^{\mathrm{4}} \left({x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)} \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }}…
Question Number 115459 by john santu last updated on 26/Sep/20 $${I}=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\sqrt[{\mathrm{3}\:}]{\mathrm{1}+{x}^{\mathrm{3}} }}\:? \\ $$$${I}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{cos}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)\:{dx}\:=\:? \\ $$$$ \\ $$…
Question Number 115449 by mathmax by abdo last updated on 25/Sep/20 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$ Answered by MJS_new last updated on…
Question Number 49903 by rahul 19 last updated on 12/Dec/18 Commented by rahul 19 last updated on 12/Dec/18 $${Period}\:{of}\:{f}\left({x}\right)=\mathrm{4}. \\ $$ Answered by mr W…
Question Number 49902 by rahul 19 last updated on 12/Dec/18 $${If}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{\:{t}} {e}^{{t}−{y}} .{ydy}. \\ $$$${Prove}\:{that}\:{F}\left({t}\right)=\:{e}^{{t}} −\left(\mathrm{1}+{t}\right). \\ $$ Commented by Abdo msup. last updated…
Question Number 49898 by Raj Singh last updated on 12/Dec/18 Commented by Abdo msup. last updated on 12/Dec/18 $${I}\:=\int_{\mathrm{1}} ^{\mathrm{400}\left[{x}\right]} \:\:{e}^{\left[{t}\right]} {dt}\:=\sum_{{k}=\mathrm{1}} ^{\mathrm{400}\left[{x}\right]−\mathrm{1}} \:\int_{{k}} ^{{k}+\mathrm{1}}…
Question Number 49838 by MJS last updated on 11/Dec/18 $$\int\frac{{dx}}{\:\sqrt{\left({a}+\mathrm{1}\right)\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{4cos}\:{x}\:−{a}+\mathrm{3}}}=? \\ $$ Commented by MJS last updated on 11/Dec/18 $$\int\frac{{dx}}{\:\sqrt{\left({a}+\mathrm{1}\right)\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{4cos}\:{x}\:−{a}+\mathrm{3}}}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\mathrm{2}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{dt}}{\:\sqrt{\left({a}+\mathrm{1}\right)\mathrm{cos}\:\mathrm{4}{t}\:+\mathrm{4cos}\:\mathrm{2}{t}\:−{a}+\mathrm{3}}}= \\…
Question Number 115366 by Bird last updated on 25/Sep/20 $${calculate}\:\int_{−\mathrm{1}} ^{\mathrm{2}} \:\frac{{dx}}{{ch}^{\mathrm{2}} {x}\:+{sh}^{\mathrm{2}} {x}} \\ $$ Answered by MJS_new last updated on 25/Sep/20 $$\int\frac{{dx}}{\mathrm{cosh}^{\mathrm{2}} \:{x}\:+\mathrm{sinh}^{\mathrm{2}}…