Question Number 48178 by Abdo msup. last updated on 20/Nov/18 $${find}\:\:\int\:\:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{3}\:+{cos}\left(\mathrm{2}\pi{x}\right)}{dx} \\ $$ Commented by Abdo msup. last updated on 25/Nov/18 $${A}=\int\:\:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{3}+{cos}\left(\mathrm{2}\pi{x}\right)}{dx}\:=_{\pi{x}\:={t}} \:\:\frac{\mathrm{1}}{\pi}\int\:\:\:\frac{{sin}\left({t}\right)}{\mathrm{3}+{cos}\left(\mathrm{2}{t}\right)}{dt} \\ $$$$\:\int\:\:\:\frac{{sin}\left({t}\right)}{\mathrm{3}\:+\mathrm{2}{cos}^{\mathrm{2}}…
Question Number 48175 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{{sin}\left({t}\right)}{dt} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 179244 by Acem last updated on 27/Oct/22 $${Evaluate}\:\int\mathrm{tan}^{\mathrm{4}} \:{x}\:\mathrm{sec}^{\mathrm{5}} \:{x}\:{dx} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 27/Oct/22 $${I}=\int\mathrm{tan}^{\mathrm{4}} {x}\mathrm{sec}^{\mathrm{5}} {xdx}=\int\mathrm{tan}^{\mathrm{3}} {x}\mathrm{sec}^{\mathrm{4}}…
Question Number 48173 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int\:\:\frac{{arctan}\left({x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by maxmathsup by imad last updated on 26/Nov/18 $${changement}\:{x}={tant}\:{give}\:\:{I}\:=\:\int\:\frac{{t}}{\:\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} {t}}}\:\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 48172 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left(\mathrm{2}{cos}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by Abdo msup. last updated on 25/Nov/18…
Question Number 48170 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 48171 by Abdo msup. last updated on 20/Nov/18 $${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}}…