Question Number 94625 by i jagooll last updated on 20/May/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{ln}\:\left(\Gamma\left({x}\right)\:{dx}\:=?\right. \\ $$$${note}\:\Gamma\left({x}\right)\::\mathrm{Gamma}\:\mathrm{function} \\ $$ Commented by turbo msup by abdo last updated…
Question Number 29079 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:{w}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{arcsin}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{find}\:{w}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29077 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{find}\:{a}\:{simple} \\ $$$${form}\:{of}\:\:{g}^{'} \left({x}\right)\:{without}\:{integral}. \\ $$ Commented by abdo imad last…
Question Number 29078 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:\:{h}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{arctan}\left({xt}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:{find}\:{h}\left({x}\right)\:. \\ $$ Commented by abdo imad last updated on 10/Feb/18 $${e}\:{have}\:{h}^{'}…
Question Number 29076 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{find}\:{asimple} \\ $$$${form}\:{of}\:{f}\left({x}\right)\:{without}\:{integral}. \\ $$ Commented by abdo imad last updated…
Question Number 94609 by M±th+et+s last updated on 20/May/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{\mathrm{2}{x}+\mathrm{3}}}{dx} \\ $$ Answered by mathmax by abdo last updated on 20/May/20 $$\mathrm{I}\:=\int\:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{2x}+\mathrm{3}}}\mathrm{dx}\:\Rightarrow\mathrm{I}\:=\int\:\frac{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\sqrt{\mathrm{2x}+\mathrm{3}}−\sqrt{\mathrm{x}+\mathrm{1}}\right)}{\mathrm{x}+\mathrm{2}}\mathrm{dx}…
Question Number 29043 by yesaditya22@gmail.com last updated on 03/Feb/18 $$\int\mathrm{tan}^{−} \left(\mathrm{1}−\mathrm{sinx}/\mathrm{1}+\mathrm{sinx}\right)\:\mathrm{dx} \\ $$ Commented by abdo imad last updated on 03/Feb/18 $${let}\:{put}\:{I}=\:\int\:{arctan}\left(\frac{\mathrm{1}−{sinx}}{\mathrm{1}+{sinx}}\right){dx}\:\:\:\left({arctan}={tan}^{−\mathrm{1}} \right){we}\:{have} \\ $$$$\frac{\mathrm{1}−{sinx}}{\mathrm{1}+{sinx}}=\frac{\mathrm{1}\:−{cos}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}{\mathrm{1}+{cos}\left(\frac{\pi}{\mathrm{2}}−{x}\right)}=\frac{\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 160113 by mnjuly1970 last updated on 25/Nov/21 $$ \\ $$$$\:\:{prove}\:\: \\ $$$$\:\:\:\:\:\:\Phi:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sinh}\left({x}\right)}{{cosh}^{\mathrm{2}} \left({x}\right)}.\frac{\mathrm{1}}{{x}}\:{dx}\:\overset{???} {=}\:\frac{\mathrm{4G}}{\pi} \\ $$ Answered by mindispower last updated…
Question Number 29038 by abdo imad last updated on 03/Feb/18 $${find}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({at}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$ Commented by abdo imad last updated on 11/Feb/18 $${let}\:{put}\:{I}\left({a}\right)=\:\underset{−\infty}…
Question Number 94574 by student work last updated on 19/May/20 $$\int\frac{\sqrt{\mathrm{cosx}}}{\:\sqrt{\mathrm{sinx}\:}\:+\sqrt{\mathrm{cosx}}}\mathrm{dx}=? \\ $$ Commented by student work last updated on 19/May/20 $$\mathrm{please}\:\mathrm{solve}\:\mathrm{who}\:\mathrm{can}? \\ $$ Answered…