Category: Integration

Question Number 66403 by ~ À ® @ 237 ~ last updated on 14/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 131919 by Algoritm last updated on 09/Feb/21 Answered by Dwaipayan Shikari last updated on 09/Feb/21 $${x}={u}^{\mathrm{6}} \\ $$$$=\mathrm{6}\int\frac{{u}^{\mathrm{5}} }{{u}^{\mathrm{2}} +{u}^{\mathrm{3}} }{du}=\mathrm{6}\int\frac{{u}^{\mathrm{3}} }{{u}+\mathrm{1}}{du}=\mathrm{6}\int\left({u}^{\mathrm{2}} −{u}+\mathrm{1}\right){du}−\mathrm{6}{log}\left({u}\right)…

Question Number 66350 by mathmax by abdo last updated on 12/Aug/19 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\sqrt{\frac{{x}^{{n}} }{\mathrm{2}+{x}^{{n}} }}\right){dx}\:\:\:\:{n}\in{N} \\ $$ Commented by mathmax by abdo last updated…

Question Number 66351 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{{nt}} }{\left(\mathrm{1}+{e}^{{t}} \right)^{{n}+\mathrm{1}} }{dt}\:\:\:\:\:\left({n}\:{from}\:{N}^{\bigstar} \right) \\ $$$$\left.\right){prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:{I}_{{n}} \\…

Question Number 66349 by mathmax by abdo last updated on 12/Aug/19 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }{dx} \\ $$ Commented by mathmax by abdo last updated…