Question Number 65740 by rajesh4661kumar@gmail.com last updated on 03/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{\frac{\mathrm{1}}{{cosx}}\:+{sinx}}\:\Rightarrow\:{A}\:=\int\:\frac{{cosx}}{\mathrm{1}+{cosx}\:{sinx}}{dx}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}\:}\right)\:={t}\:{give}\:{A}\:=\int\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 65736 by malwaan last updated on 03/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}\:+\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:? \\ $$ Commented by Souvik Ghosh last updated on 03/Aug/19 $${let}\:\:\:{u}=\mathrm{2}{x}\Leftrightarrow{du}=\mathrm{2}{dx} \\…
Question Number 191 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:\underset{\mathrm{C}} {\int}\frac{{z}^{\mathrm{2}} \mathrm{sin}\:{z}\:\mathrm{cos}\:{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)\left({z}^{\mathrm{2}} −\mathrm{1}\right)}{dz}\: \\ $$$$\mathrm{where}\:\mathrm{C}=\left\{{z}\in\mathbb{C}\mid\mid{z}\mid=\mathrm{2}\right\} \\ $$ Answered by nileshkulkarni last updated on 15/Dec/14…
Question Number 65726 by aliesam last updated on 02/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65729 by aliesam last updated on 02/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$\left.{a}\right)\:\:{let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{{ix}} \:{x}^{−\alpha} \:{dx}\:\:\Rightarrow{f}\left(\alpha\right)\:=_{{ix}\:={t}} \:\:\:\int_{\mathrm{0}} ^{\infty}…
Question Number 131245 by Ahmed1hamouda last updated on 02/Feb/21 $$\:\mathrm{Find}\: \\ $$$$\:\:\:\:\int_{−\mathrm{b}} ^{\mathrm{b}} \int_{−\mathrm{a}} ^{\mathrm{a}} \frac{\mathrm{d}{xdy}}{\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{h}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} } \\ $$ Answered by Ar…
Question Number 131247 by bramlexs22 last updated on 03/Feb/21 $$\left(\mathrm{1}\right)\:\psi\:=\:\int\:\frac{{dx}}{\mathrm{1}−\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}=? \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}}{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}\:=? \\ $$$$\left(\mathrm{3}\right)\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{3}/\mathrm{2}} +\mathrm{1}}\:{dx}\:=?\: \\ $$ Answered by liberty…
Question Number 65704 by mmkkmm000m last updated on 03/Aug/19 $$\int{ln}^{\mathrm{2}} {xsin}\left({x}\right){dx} \\ $$ Commented by Tinku Tara last updated on 02/Aug/19 $$\mathrm{Can}\:\mathrm{please}\:\mathrm{use}\:\mathrm{smaller}\:\mathrm{font}\:\mathrm{size} \\ $$ Terms…
Question Number 164 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:{f}\left({a},{b}\right)=\underset{{a}} {\overset{{b}} {\int}}\left({b}−{x}\right)\left({x}−{a}\right){dx} \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\left({b}−{x}\right)\left({x}−{a}\right)=−{x}^{\mathrm{2}} +\left({a}+{b}\right){x}−{ab} \\…
Question Number 131227 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{real}\:\:{analysis}\:… \\ $$$$\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\boldsymbol{\Omega}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({ln}\left(\frac{\mathrm{1}}{{x}}\right)\right){ln}^{\mathrm{2}} \left({x}\right){dx}=\mathrm{3}−\mathrm{2}\gamma \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…