Question Number 30182 by abdo imad last updated on 17/Feb/18 $${find}\:\int_{\mathrm{2}} ^{\mathrm{3}} \:\:\:\frac{\sqrt{{x}+\mathrm{1}}}{{x}\sqrt{\mathrm{1}−{x}}}{dx}\:. \\ $$ Commented by abdo imad last updated on 21/Feb/18 $${let}\:{put}\:\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}\:={t}\:\Leftrightarrow\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\:={t}^{\mathrm{2}} \:\:\Leftrightarrow{x}+\mathrm{1}=−{t}^{\mathrm{2}}…
Question Number 30184 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanx}\:{dx}\:.\:\left({arctan}={tan}^{−\mathrm{1}} \right). \\ $$ Commented by abdo imad last updated on 20/Feb/18…
Question Number 30181 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} \:+{x}^{\mathrm{6}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30179 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int\:\:\:\:\frac{{dt}}{\mathrm{1}+{cost}\:+{sint}}\:\:. \\ $$ Commented by abdo imad last updated on 24/Feb/18 $${the}\:{ch}.\:{tan}\left(\frac{{t}}{\mathrm{2}}\right)={x}\:{give}\: \\ $$$${I}\:=\:\int\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 30180 by abdo imad last updated on 17/Feb/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}\:{sinx}\:{cosx}}{{tan}^{\mathrm{2}} {x}\:+{cotan}^{\mathrm{2}} {x}}{dx}\:.\left({use}\:{the}\:{ch}.{x}=\frac{\pi}{\mathrm{2}}\:−{t}\right). \\ $$ Commented by abdo imad last updated on 24/Feb/18…
Question Number 30178 by abdo imad last updated on 17/Feb/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:{cos}\theta}\:\:{with}\:−\pi<\theta<\pi\:. \\ $$ Commented by prof Abdo imad last updated on 22/Feb/18 $${let}\:{put}\:{cos}\theta={t}\:{I}=\:\int_{\mathrm{0}}…
Question Number 161233 by cortano last updated on 14/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161229 by cortano last updated on 14/Dec/21 $$\:{Given}\:{f}\left({x}\right)=\:\begin{cases}{\mathrm{1}−\mid{x}\mid\:;\:{x}\leqslant\mathrm{1}}\\{\mid{x}\mid−\mathrm{1}\:;\:{x}>\mathrm{1}}\end{cases} \\ $$$$\:{find}\:\int_{−\mathrm{3}} ^{\:\mathrm{8}} \left[{f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)\right]\:{dx}.\: \\ $$ Answered by mr W last updated on 14/Dec/21 Commented…
Question Number 95692 by mathmax by abdo last updated on 27/May/20 $$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{xsin}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 95690 by mathmax by abdo last updated on 27/May/20 $$\mathrm{calculate}\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{cos}^{\mathrm{3}} \left(\mathrm{x}\right)\mathrm{sh}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{dx}\:\mathrm{and}\:\mathrm{J}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\mathrm{sin}^{\mathrm{3}} \mathrm{x}\:\mathrm{ch}^{\mathrm{2}} \mathrm{x} \\ $$ Terms of Service…