Question Number 48171 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by Abdo msup. last updated on 21/Nov/18 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 113675 by AbhishekBasnet last updated on 14/Sep/20 Commented by mohammad17 last updated on 14/Sep/20 $$\left.=−\:\frac{\mathrm{1}}{{b}}\int\left(\left({a}−{bx}\right)−{a}\right)\left({a}−{bx}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \right){dx} \\ $$$$ \\ $$$$=−\frac{\mathrm{1}}{{b}}\int\left(\left({a}−{bx}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} −{a}\left({a}−{bx}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \right){dx} \\…
Question Number 48127 by cesar.marval.larez@gmail.com last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\left.\mathrm{30}\right){t}=\frac{−\mathrm{1}}{{x}}\:\:\:{dt}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} }{dx} \\ $$$$\int{e}^{{t}} {dt}={e}^{{t}} +{c} \\ $$$${e}^{{t}} +{c}…
Question Number 113656 by bobhans last updated on 14/Sep/20 $$\:\:\int\:\frac{\left(\mathrm{1}+\mathrm{tan}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} }{\mathrm{1}+\mathrm{sin}\:\mathrm{3x}}\:\mathrm{dx}\:? \\ $$ Answered by john santu last updated on 14/Sep/20 $$\:{setting}\:\mathrm{tan}\:\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)\:=\:{s}\:\rightarrow\mathrm{sin}\:\mathrm{3}{x}\:=\:\frac{\mathrm{2}{s}}{\mathrm{1}+{s}^{\mathrm{2}} } \\ $$$$\mathrm{1}+\mathrm{sin}\:\mathrm{3}{x}\:=\:\frac{\left(\mathrm{1}+{s}\right)^{\mathrm{2}}…
Question Number 179194 by Acem last updated on 26/Oct/22 $${Evaluate}\:{the}\:\int\:\frac{\mathrm{tan}^{\mathrm{5}} \:{x}}{\mathrm{cos}^{\mathrm{9}} \:{x}}\:{dx} \\ $$ Answered by Acem last updated on 26/Oct/22 $${Deuxie}'{me}\:{methode}: \\ $$$$\int\:\frac{\mathrm{tan}^{\mathrm{5}} \:{x}}{\mathrm{cos}^{\mathrm{9}}…
Question Number 179181 by neinhaltsieger369 last updated on 26/Oct/22 $$\:\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\:\mathrm{Use}\:\mathrm{double}\:\mathrm{integral}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{following}\:\mathrm{curves}\: \\ $$$$\:\mathrm{given}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{shown}\:\mathrm{below}: \\ $$$$\: \\ $$$$\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4x}\:\mathrm{and}\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:=\:\mathrm{4y} \\…
Question Number 48104 by wasim last updated on 19/Nov/18 $$\mathrm{solve}\:\mathrm{this}\:\: \\ $$$$\int\left(\mathrm{2}\:\mathrm{sinx}+\mathrm{cosx}\right)/\left(\mathrm{2}+\mathrm{3sinx}+\mathrm{sin}^{\mathrm{2x}} \right)\:\mathrm{dx} \\ $$ Answered by MJS last updated on 19/Nov/18 $$\mathrm{Weierstrass}−\mathrm{substitution} \\ $$$${t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\Rightarrow\:{x}=\mathrm{2arctan}\:{t};\:{dx}=\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 179175 by Acem last updated on 26/Oct/22 $$\:{Find}\:\int{x}^{\mathrm{5}} \:\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$$$\:{Answer}:\:{I}=\:\frac{\mathrm{2}}{\mathrm{45}}\:\left(\mathrm{3}{x}^{\mathrm{3}} −\mathrm{2}\right)\:\sqrt{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:+\:{c} \\ $$$$ \\ $$ Commented by…
Question Number 113634 by eric last updated on 14/Sep/20 $${Bonjour}\:{besoin}\:{d}'{aide} \\ $$$${Calculer}\:\int{ln}\left({cosx}\right){dx} \\ $$ Answered by Olaf last updated on 14/Sep/20 $$\mathrm{cos}{x}\:=\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} {x}^{\mathrm{2}{k}}…
Question Number 113630 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{explicit}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}\left(\mathrm{1}+\mathrm{acos}^{\mathrm{2}} \theta\right)\mathrm{d}\theta \\ $$ Answered by Dwaipayan Shikari last updated on 15/Sep/20…