Question Number 218563 by Nicholas666 last updated on 12/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{solve}\:{for}\:\boldsymbol{{x}}\:\in\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({xt}\right)}{{e}^{{t}} −\mathrm{1}\:}\:{dt}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\:{coth}\left(\boldsymbol{\pi}{x}\right)\:−\:\frac{\mathrm{1}}{\mathrm{2}{x}}\:\: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 218594 by MrGaster last updated on 12/Apr/25 $$\mathrm{A}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{calculation}\:\mathrm{relatedt} \\ $$$$\mathrm{o}\:\mathrm{arctangent}\:\mathrm{integral}: \\ $$$$\boldsymbol{\mathrm{Exere}}:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{arctan}^{\mathrm{2}} }{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}. \\ $$$$\mathrm{Solution}:\underset{{A}} {\underbrace{=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{arctan}^{\mathrm{2}} {x}}{{x}}{dx}}}\:−\underset{{B}} {\underbrace{\int_{\mathrm{0}}…
Question Number 218462 by York12 last updated on 10/Apr/25 $$\int\frac{{dx}}{\:\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} +\mathrm{3}}} \\ $$ Answered by som(math1967) last updated on 10/Apr/25 $$\int\frac{{dx}}{\:\sqrt{\mathrm{4}−\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\right)}} \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{2}^{\mathrm{2}} −\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 218398 by Nicholas666 last updated on 09/Apr/25 Answered by MrGaster last updated on 10/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 218376 by Nicholas666 last updated on 08/Apr/25 $$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{J}}_{\boldsymbol{\alpha}} \left(\boldsymbol{{ar}}\right)}{\left(\boldsymbol{{r}}^{\mathrm{2}} +\boldsymbol{{k}}^{\mathrm{2}} \right)\boldsymbol{\mu}}\boldsymbol{{dr}}\: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 218383 by Nicholas666 last updated on 08/Apr/25 Commented by Nicholas666 last updated on 08/Apr/25 $${please}\:{check}\:{where}\:{My}\:{mistakes},{friend} \\ $$ Commented by vnm last updated on…
Question Number 218375 by Nicholas666 last updated on 08/Apr/25 $$ \\ $$$$\:\:\int\frac{\sqrt{\boldsymbol{{tan}}\:\boldsymbol{{x}}}}{\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$$$ \\ $$ Answered by Ghisom last updated on 08/Apr/25 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}^{\mathrm{3}}…
Question Number 218374 by Nicholas666 last updated on 08/Apr/25 $$\: \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \boldsymbol{{J}}_{\alpha} \left(\sqrt{\boldsymbol{{ar}}}\right)\boldsymbol{{e}}^{−\boldsymbol{{r}}} \boldsymbol{{dr}}\: \\ $$$$\: \\ $$ Terms of Service Privacy Policy…
Question Number 218322 by shunmisaki007 last updated on 06/Apr/25 $$\mathrm{Evaluate}\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\left({x}\right)}{\mathrm{sin}^{\mathrm{3}} \left({x}\right)+\mathrm{cos}^{\mathrm{3}} \left({x}\right)}\:{dx}. \\ $$ Answered by Ghisom last updated on 06/Apr/25 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{3}}…