Question Number 18281 by aplus last updated on 17/Jul/17 Answered by Tinkutara last updated on 18/Jul/17 $$\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{sin}\:\mathrm{2}{x}\:{dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{−\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}\right)\:=\:\frac{−\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{4}}\:+\:{C} \\ $$ Answered by mrW1 last…
Question Number 83807 by niroj last updated on 06/Mar/20 $$\:\:\boldsymbol{\mathrm{Evaluate}}: \\ $$$$\:\:\int\:\:\frac{\:\mathrm{1}}{\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{c}}}\boldsymbol{\mathrm{dx}} \\ $$ Commented by mathmax by abdo last updated on 06/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{{ax}^{\mathrm{2}}…
Question Number 83805 by M±th+et£s last updated on 06/Mar/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Mar/20 $${A}\:=\int_{\mathrm{0}}…
Question Number 149329 by mnjuly1970 last updated on 04/Aug/21 Commented by Kamel last updated on 04/Aug/21 $${I}\:{think}\:{I}^{\mathrm{100}} +{k}\equiv\mathrm{0}\left[\mathrm{14}\right] \\ $$ Answered by Kamel last updated…
Question Number 83781 by john santu last updated on 06/Mar/20 $$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$ Commented by niroj last updated on 06/Mar/20 $$\:\:\int_{\mathrm{0}}…
Question Number 18232 by Joel577 last updated on 17/Jul/17 $$\mathrm{If}\:{f}\left({x}\right)\:=\:\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}\sqrt{}…}}}} \\ $$$$\mathrm{find}\:\int\:{f}\left({x}\right)\:{dx} \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}{f}\left({x}\right)}}…
Question Number 18233 by Joel577 last updated on 17/Jul/17 $$\mathrm{If}\:{y}\:=\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{…}}}} \\ $$$$\mathrm{find}\:\int\left({y}\:+\:\sqrt{{y}}\right)\:{dx} \\ $$ Commented by alex041103 last updated on 17/Jul/17 $${did}\:{you}\:{mean}\:{y}=\sqrt{{x}^{\mathrm{2}}…
Question Number 18223 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\pi} \frac{\mathrm{x}\:\mathrm{tanx}}{\mathrm{tanx}+\mathrm{secx}}\mathrm{dx}=\frac{\pi}{\mathrm{2}}\left(\pi−\mathrm{2}\right) \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${First}\:{we}\:{will}\:{integrate}\:{by}\:{parts} \\ $$$${u}={x}\:\:\:\:{dv}=\frac{{tan}\:{x}}{{tan}\:{x}\:+\:{sec}\:{x}}…
Question Number 18224 by Arnab Maiti last updated on 17/Jul/17 $$\int\mathrm{cos2x}\:\mathrm{ln}\left(\mathrm{1}+\mathrm{tanx}\right)\mathrm{dx} \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${We}\:{integrate}\:{by}\:{parts} \\ $$$${u}={ln}\left(\mathrm{1}+{tan}\:{x}\right)\:\:\:{dv}={cos}\mathrm{2}{x} \\ $$$${du}=\frac{{sec}^{\mathrm{2}}…
Question Number 18222 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{x}\:\mathrm{sinx}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=\frac{\pi}{\mathrm{4}} \\ $$ Commented by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{these}\:\mathrm{questions}.…