Category: Integration

Question Number 218879 by Nicholas666 last updated on 16/Apr/25 $$$$$$\mathit{C}\mathit{a}\mathit{l}\mathit{c}\mathit{u}\mathit{l}\mathit{a}\mathit{t}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{f}\mathit{o}\mathit{l}\mathit{l}\mathit{o}\mathit{w}\mathit{i}\mathit{n}\mathit{g}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{g}\mathit{r}\mathit{a}\mathit{l};$$$$\:\:\int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \boldsymbol{{xJ}}_{\mathrm{0}} \left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }\right)\boldsymbol{{J}}_{\mathrm{1}} \left(\sqrt{\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}}…

Question Number 218866 by Nicholas666 last updated on 16/Apr/25 $$$$$$evaluatethefollowingintegralinclosedformorexpress$$$$itintermsofknownspecialfunctions;$$$${\int }_{}^{\mathrm{\infty }}{\mathit{K}}_{\mathit{i}\mathit{\lambda }}\left(\mathit{a}\mathit{t}\right){\mathit{J}}_{\mathit{\nu }}{\left(\mathit{b}\mathit{t}\right)}^{\mathit{\mu }-1}\mathit{d}\mathit{t}$$$$\:\boldsymbol{{where}}; \…

Question Number 218780 by Spillover last updated on 15/Apr/25 Commented by malwan last updated on 17/Apr/25 $$canyousolvethisintegral$$$$please?$$ Answered by Spillover last…

Question Number 218779 by Spillover last updated on 15/Apr/25 Answered by breniam last updated on 15/Apr/25 $$$$$$\int \frac{1}{1+\cosh x}\mathrm{d}x=\int \frac{1}{1+\frac{e^x+e^{-x}}{2}}\mathrm{d}x=\int \frac{2}{e^x+2+e^{-x}}\mathrm{d}x=$$$$\int\frac{\mathrm{2}}{\left({e}^{\frac{{x}}{\mathrm{2}}}…

Question Number 218674 by Spillover last updated on 14/Apr/25 Answered by Nicholas666 last updated on 14/Apr/25 $$\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}^{\mathrm{4}} }{\:\sqrt{\mathrm{8}+\mathrm{2}{x}^{\mathrm{2}} −{x}^{\mathrm{4}} \:}}\right)\sqrt{\frac{\mathrm{2}+{x}^{\mathrm{2}} }{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}…