Question Number 52484 by Tawa1 last updated on 08/Jan/19 $$\int\:\:\frac{\mathrm{cos}\:\mathrm{x}\:−\:\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 $$\int\frac{{dx}}{{x}}−\int{tanxdx} \\ $$$${lnx}−{lnsecx}+{c} \\ $$ Commented…
Question Number 52482 by maxmathsup by imad last updated on 08/Jan/19 $${find}\:{the}\:{value}\:{or}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:. \\ $$ Commented by Abdo msup. last updated on…
Question Number 118010 by TANMAY PANACEA last updated on 14/Oct/20 $$\int\frac{{dx}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}} \\ $$ Commented by mmmmmm1 last updated on 14/Oct/20 $$\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\frac{\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)}\right]=\:\frac{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\centerdot\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\right]\:−\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\centerdot\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left[\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\right]}{\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)^{\mathrm{2}} } \\…
Question Number 52459 by Abdo msup. last updated on 08/Jan/19 $${let}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{i}\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{ix}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{ix}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}. \\…
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Question Number 117979 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mid\:\:\Gamma\:\left(\:{i}\:\right)\:\mid\overset{?} {=}\:\sqrt{\frac{\pi}{{sinh}\left(\pi\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\Gamma:\:\mathscr{E}{uler}\:{gamma}\:{function}\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Commented by…
Question Number 117963 by peter frank last updated on 14/Oct/20 Answered by john santu last updated on 14/Oct/20 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \left({x}^{\mathrm{3}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} \:}\:\right){dx}\:=\:\mathrm{0} \\ $$$${then}\:\int_{−\mathrm{2}}…
Question Number 52418 by Abdo msup. last updated on 07/Jan/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 08/Jan/19…
Question Number 117948 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{integral}…\: \\ $$$$\:\:\:{please}\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({sin}\left({x}\right)+{sin}\left(\frac{\mathrm{1}}{{x}}\right)\right)\frac{{dx}}{{x}}\:=?? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\:\: \\…
Question Number 117944 by bemath last updated on 14/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{satisfies}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\left(\frac{\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{x}}}{\:\sqrt{\mathrm{2k}}}\:\right)\:\mathrm{dx}\:=\:\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$ \\ $$ Answered by john santu last updated on…