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Category: Integration

1-dx-x-2-x-

Question Number 183559 by cortano1 last updated on 27/Dec/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{{dx}}{{x}^{\mathrm{2}} +\sqrt{{x}}}\:=\:?\: \\ $$ Answered by greougoury555 last updated on 27/Dec/22 $$\:\:\:{G}\:=\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{2}}…

cos-x-x-sin-x-x-cos-x-dx-

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…

dx-x-4-x-2-1-

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}} } \\…

let-f-0-1-ln-1-i-x-1-x-2-dx-1-determine-a-explicit-form-of-f-2-calculate-0-1-ln-1-ix-1-x-2-dx-and-0-1-ln-1-2ix-1-x-2-dx-

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}. \\…

nice-calculus-prove-that-i-pi-sinh-pi-Euler-gamma-function-m-n-july-1970-

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-117963

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}}…

nice-integral-please-evaluate-I-0-1-sin-x-sin-1-x-dx-x-m-n-1970-

Question Number 117948 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{integral}…\: \\ $$$$\:\:\:{please}\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({sin}\left({x}\right)+{sin}\left(\frac{\mathrm{1}}{{x}}\right)\right)\frac{{dx}}{{x}}\:=?? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\:\: \\…