Menu Close

Category: Integration

old-and-unanswered-Mr-Mathdave-x-2-ln-1-x-ln-1-x-dx-

Question Number 114044 by Her_Majesty last updated on 16/Sep/20 $${old}\:{and}\:{unanswered}…\:{Mr}\:{Mathdave}??? \\ $$$$\int{x}^{\mathrm{2}} {ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right){dx}=? \\ $$ Answered by mathdave last updated on 17/Sep/20 $${sokution} \\ $$$${put}\:{x}=\left(\mathrm{2}{y}−\mathrm{1}\right)\:\:\left({wat}\:{i}\:{did}\:{here}\:{is}\:{logical}\right)…

advanced-calculus-i-prove-that-0-1-ln-1-ln-1-x-ln-1-x-dx-n-1-n-1-n-2-ii-prove-that-0-1-ln-1-x-x-1

Question Number 114045 by mnjuly1970 last updated on 17/Sep/20 $$\:\:\:\:\:\:\:\:…\:\:{advanced}\:{calculus}… \\ $$$$ \\ $$$${i}\::\:\:{prove}\:\:{that}\::: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}−{x}\right)\right)}{{ln}\left(\mathrm{1}−{x}\right)}\:{dx}\:\overset{?} {=}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\Gamma\left({n}+\mathrm{1}\right)}{{n}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${ii}:\: \\…

find-A-n-0-pi-4-cos-n-xdx-and-B-n-0-pi-4-sin-n-xdx-2-find-0-pi-4-cos-6-xdx-and-0-pi-4-sin-6-xdx-

Question Number 48498 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{{n}} {xdx}\:\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{\mathrm{6}} {xdx}\:{and}\:\int_{\mathrm{0}}…

let-f-x-0-1-ln-1-xt-2-1-t-2-dt-1-find-a-xplicit-form-of-f-x-2-developp-f-at-integr-serie-3-find-the-value-of-0-1-ln-1-t-2-1-t-2-dt-4-find-the-value-of-0-1-ln-1-2t-2

Question Number 48497 by maxmathsup by imad last updated on 24/Nov/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{xplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\: \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…

prove-that-0-1-t-3-4-1-t-1-4-t-dt-is-convergent-and-find-its-value-

Question Number 48491 by maxmathsup by imad last updated on 24/Nov/18 $${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{{t}}{dt}\:{is}\:{convergent}\:{and}\:{find}\:{its}\:{value}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-48484

Question Number 48484 by Meritguide1234 last updated on 24/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18 $${trying}\:{to}\:{solve} \\ $$$${let}\:{in}\:{place}\:{of}\:\sqrt{\mathrm{3}}\:\:{putting}\:\:{a}\:\:\:\:\:{a}=\sqrt{\mathrm{3}}\: \\ $$$${finding}\:{the}\:{values}\:{of}\:{x}\:\:{so}\:{that} \\ $$$${sinax}={sinx} \\ $$$${ax}={k}\pi+\left(−\mathrm{1}\right)^{{k}}…