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Category: Integration

If-f-x-x-2-3-x-2-3-find-f-x-dx-

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)}}…

If-y-x-2-x-2-x-2-find-y-y-dx-

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}}…

prove-that-0-pi-x-tanx-tanx-secx-dx-pi-2-pi-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}}…

cos2x-ln-1-tanx-dx-

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}}…

show-that-0-pi-4-x-sinx-1-cos-2-x-dx-pi-4-

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}.…