Category: Integration

Question Number 34109 by tanmay.chaudhury50@gmail.com last updated on 30/Apr/18 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 99576 by mathmax by abdo last updated on 21/Jun/20 $$1)\mathrm{let}\mathrm{f}\left(\mathrm{a}\right)={\int }_0^{\mathrm{\infty }}\frac{{\mathrm{t}}^{\mathrm{a}-1}\ln \left(\mathrm{t}\right)}{1+\mathrm{t}}\mathrm{dt}\mathrm{with}0<\mathrm{a}<1\mathrm{prove}\mathrm{that}\mathrm{f}\left(\mathrm{a}\right)\mathrm{is}\mathrm{convergent}\mathrm{and}\mathrm{determine}$$$$\mathrm{it}\mathrm{value}$$$$2)\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{lnt}}{(1+\mathrm{t})\sqrt{\mathrm{t}}}\mathrm{dt}$$$$\left.\mathrm{3}\right)\mathrm{calculate}\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnt}}{\left(^{\mathrm{3}}…

Question Number 165097 by abdullahhhhh last updated on 26/Jan/22 Answered by Eulerian last updated on 26/Jan/22 $$$$$$\mathrm{By}\mathrm{using}\mathrm{King}\mathrm{rule}\mathrm{of}\mathrm{integration}:$$$$\:\int_{\frac{\pi}{\mathrm{6}}\:} ^{\:\frac{\pi}{\mathrm{3}}} \:\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)} } \:−\:\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)}…

Question Number 99557 by adeyemi last updated on 21/Jun/20 $$$$$$\mathrm{\Lambda }={\int }_0^1({\mathrm{Li}}_2\left(\frac{1}{1+\mathrm{x}}\right)+{\mathrm{Li}}_3\left(\frac{\mathrm{x}}{1+\mathrm{x}}\right)+{\mathrm{Li}}_4\left(\frac{\mathrm{x}+1}{{\mathrm{x}}^2+\mathrm{x}+1}\right))\mathrm{dx}$$$${\mathrm{Li}}_{\mathrm{n}}\left(\mathrm{z}\right)=\mathrm{polylogarithm}\mathrm{function}.$$$$\mathrm{by}\mathrm{adeyemi}.$$$$…

Question Number 99541 by student work last updated on 21/Jun/20 $${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\mathrm{e}}^{-{2\mathrm{x}}^2-5\mathrm{x}-3}\mathrm{dx}=?$$$$\mathrm{help}\mathrm{me}$$ Answered by smridha last updated on…