Question Number 259 by a@b.c last updated on 25/Jan/15 $$\int_{{a}} ^{{b}} \:\frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx}= \\ $$ Answered by prakash jain last updated on 17/Dec/14 $$\mathrm{Substitue}\:{x}={a}+{b}−{y}\:\Rightarrow{dx}=−{dy} \\ $$$$\mathrm{The}\:\mathrm{given}\:\mathrm{integral}\:{I}…
Question Number 65788 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $${Explicit}\:\:\:{f}\left({a}.{b}.{c}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sec}\left({x}−{a}\right)}{{b}.{cosx}\:+\:{c}.{sinx}}\:{dx} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 65786 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $$\:{Shows}\:{that}\:\:\mid\Gamma\left(\mathrm{1}+{ix}\right)\mid^{\mathrm{2}} =\frac{\pi}{{xsinh}\left(\pi{x}\right)}\:\:\:\:\:\:{with}\:\Gamma\left({z}\right)=\int_{\mathrm{0}_{} } ^{\infty} \:{t}^{{z}−\mathrm{1}} {e}^{−{t}} {dt} \\ $$$${Then}\:{Prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\mid\Gamma\left(\mathrm{1}+{ix}\right)\mid^{\mathrm{2}}…
Question Number 243 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\underset{−\infty} {\overset{+\infty} {\int}}\frac{\mathrm{sin}\:{x}}{{x}}{dx} \\ $$ Answered by prakash jain last updated on 17/Dec/14 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{consider}\:\underset{\mathrm{0}}…
Question Number 65776 by mathmax by abdo last updated on 03/Aug/19 $${find}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cosx}}{\mathrm{2}+\mathrm{5}{sinx}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 04/Aug/19 $${u}=\mathrm{2}+\mathrm{5}{sinx}\Rightarrow{du}=\mathrm{5}{cosxdx} \\…
Question Number 65774 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {x}}{{sin}^{\mathrm{2}} \left(\frac{{nx}}{\mathrm{2}}\right)}{dx}\:\:\:\:\left({n}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 65773 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){detemine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{\left(\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)^{\mathrm{2}} }{dt} \\…
Question Number 65775 by mathmax by abdo last updated on 03/Aug/19 $$\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{tanx}}{\mathrm{2}+\mathrm{3}{cosx}}{dx} \\ $$ Commented by mathmax by abdo last updated on 04/Aug/19…
Question Number 65770 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}}…
Question Number 65769 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by ~ À ® @ 237…