Category: Integration

Question Number 18232 by Joel577 last updated on 17/Jul/17 $$\mathrm{If}f\left(x\right)=\sqrt{x^2\sqrt{3\sqrt{x^2\sqrt{3\sqrt{}\dots }}}}$$$$\mathrm{find}\int f\left(x\right)dx$$ 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 18223 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{prove}\mathrm{that}{\int }_0^{\pi }\frac{\mathrm{x}\mathrm{tanx}}{\mathrm{tanx}+\mathrm{secx}}\mathrm{dx}=\frac{\pi }{2}(\pi -2)$$ Answered by alex041103 last updated on 17/Jul/17 $$Firstwewillintegratebyparts$$$${u}={x}\:\:\:\:{dv}=\frac{{tan}\:{x}}{{tan}\:{x}\:+\:{sec}\:{x}}…

Question Number 18222 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{show}\mathrm{that}{\int }_0^{\frac{\pi }{4}}\frac{\mathrm{x}\mathrm{sinx}}{1+{\cos }^2\mathrm{x}}\mathrm{dx}=\frac{\pi }{4}$$ Commented by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{these}\:\mathrm{questions}.…

Question Number 149273 by john_santu last updated on 04/Aug/21 $${\int }_0^{\frac{\pi }{4}}\frac{{\mathrm{e}}^{\tan \mathrm{x}}\sin {}^2\mathrm{x}}{\cos {}^4\mathrm{x}}\mathrm{dx}=?$$ Answered by Ar Brandon last updated on 04/Aug/21…

Question Number 83713 by mhmd last updated on 05/Mar/20 $$\int \frac{dx}{\sqrt{x+\sqrt{x+\sqrt{x}}}}pleassirhelpme$$ Commented by niroj last updated on 05/Mar/20 $$$$$$\int \frac{1}{\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}}}}\mathrm{dx}$$$$\:=\:\int\:\frac{\:\:\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}}}\mathrm{dx}=\:\int\:\frac{\mathrm{2}}{\mathrm{1}+\sqrt{\mathrm{4x}+\mathrm{1}}}\mathrm{dx} \…