Question Number 140334 by mnjuly1970 last updated on 06/May/21 $$ \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\xi}\::=\:\int_{−\infty} ^{\:\infty} {ln}\left(\mathrm{2}−\mathrm{2}{cos}\left({x}^{\mathrm{2}} \right)\right){dx}=? \\ $$$$ \\ $$ Answered by ArielVyny last…
Question Number 74793 by mathmax by abdo last updated on 30/Nov/19 $${prove}\:{the}\:{convergence}\:{of}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}}\right)}{\:\sqrt{{x}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Dec/19…
Question Number 140330 by Satyendra last updated on 06/May/21 $${Find}\:{the}\:{Integration}\:{Value}: \\ $$$$\mathrm{1} \:\int\frac{\sqrt{{x}}{d}\left({x}\right)}{\mathrm{1}+^{\mathrm{3}} \sqrt{{x}}}=? \\ $$$$\mathrm{2} \int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} −{x}^{\frac{\mathrm{1}}{\mathrm{4}}} }=? \\ $$ Answered by john_santu last…
Question Number 140310 by liberty last updated on 06/May/21 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}\:=\:\mathrm{0} \\ $$ Answered by qaz last updated on 06/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 140282 by qaz last updated on 06/May/21 $$\underset{{k}=\mathrm{0}} {\overset{{p}−\mathrm{1}} {\sum}}\begin{pmatrix}{{p}}\\{{k}}\end{pmatrix}\mathrm{sin}\:\left[\mathrm{2}\left({p}−{k}\right){x}\right]=? \\ $$$$\begin{pmatrix}{{p}}\\{\mathrm{0}}\end{pmatrix}\mathrm{sin}\:\left(\mathrm{2}{px}\right)+\begin{pmatrix}{{p}}\\{\mathrm{1}}\end{pmatrix}\mathrm{sin}\:\left[\left(\mathrm{2}{p}−\mathrm{2}\right){x}\right]+\begin{pmatrix}{{p}}\\{\mathrm{2}}\end{pmatrix}\mathrm{sin}\:\left[\left(\mathrm{2}{p}−\mathrm{4}\right){x}\right]+…+\begin{pmatrix}{\:\:\:{p}}\\{{p}−\mathrm{1}}\end{pmatrix}\mathrm{sin}\:\left(\mathrm{2}{x}\right)=\mathrm{2}^{{p}} \centerdot\mathrm{cos}\:^{{p}} \left({x}\right)\centerdot\mathrm{sin}\:\left({px}\right)\:\:\:\:\:??? \\ $$$${or}\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\:^{{p}} \left({x}\right)\centerdot\mathrm{sin}\:\left({px}\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\mathrm{2}^{−{p}} \right)\:\:\:\:\:{why}\:??? \\ $$ Terms…
Question Number 140278 by MarhAH last updated on 06/May/21 $$\int\sqrt{{x}\:\frac{}{}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74720 by chess1 last updated on 29/Nov/19 Commented by mathmax by abdo last updated on 29/Nov/19 $${changement}\:\sqrt{\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}}\:={t}\:{give}\:{x}−\mathrm{1}\:={t}^{\mathrm{2}} \left({x}+\mathrm{1}\right)\:\Rightarrow\left(\mathrm{1}−{t}^{\mathrm{2}} \right){x}=\mathrm{1}+{t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}=\frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 9158 by geovane10math last updated on 21/Nov/16 $$\int{x}^{{x}} \:{dx}\:=\:? \\ $$ Answered by FilupSmith last updated on 22/Nov/16 $${x}^{{x}} ={e}^{{x}\mathrm{ln}\left({x}\right)} \\ $$$${e}^{{x}\mathrm{ln}\left({x}\right)} =\underset{{n}=\mathrm{0}}…
Question Number 140221 by qaz last updated on 05/May/21 $$\int_{\mathrm{0}} ^{\infty} {x}^{\mathrm{2}} \left[{ln}\left(\mathrm{1}+{e}^{{x}} \right)−{x}\right]{dx}=\frac{\mathrm{7}\pi^{\mathrm{4}} }{\mathrm{360}} \\ $$ Answered by Dwaipayan Shikari last updated on 05/May/21…
Question Number 140202 by qaz last updated on 05/May/21 $$\int_{\mathrm{0}} ^{\infty} \left(\frac{{lnx}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{2}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated on 05/May/21 $$\Phi\:=\int_{\mathrm{0}}…