Category: Integration

Question Number 79413 by rajesh4661kumar@gmail.com last updated on 25/Jan/20 Commented by john santu last updated on 25/Jan/20 $${\left(\frac{\cos x\sin x}{\cos 2x({\cos }^{2}x-\sin {}^{2}x)}\right)}^2=$$$$\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}}\:=\frac{\mathrm{1}}{\mathrm{4}}\mathrm{tan}\:^{\mathrm{2}}…

Question Number 144925 by qaz last updated on 30/Jun/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{\left(2\mathrm{n}\right)!!}{2^{\mathrm{n}}\cdot (\mathrm{n}+1)\cdot (2\mathrm{n}+1)!!}=?$$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}\right)!!=\mathrm{2n}\left(\mathrm{2n}−\mathrm{2}\right)\left(\mathrm{2n}−\mathrm{4}\right)…=\mathrm{2}^{\mathrm{n}} \mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)…=\mathrm{2}^{\mathrm{n}}…

Question Number 144924 by qaz last updated on 30/Jun/21 $$\mathrm{S}\left(\mathrm{x}\right)=\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{\left(2\mathrm{n}\right)!!}{(2\mathrm{n}+1)!!}{\mathrm{x}}^{2\mathrm{n}}=?\dots \dots ..(\mid \mathrm{x}\mid <1)$$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}+\mathrm{1}\right)!!=\frac{\left(\mathrm{2n}+\mathrm{1}\right)!}{\left(\mathrm{2n}\right)!!} \…

Question Number 144905 by SLVR last updated on 30/Jun/21 Commented by SLVR last updated on 30/Jun/21 $$kindlyhelpme$$ Terms of Service Privacy Policy Contact:…

Question Number 144896 by physicstutes last updated on 30/Jun/21 $$\mathrm{Evaluate}$$$$\int e^x{\left(\frac{1-x}{1+x^2}\right)}^{2}dx$$ Answered by Dwaipayan Shikari last updated on 30/Jun/21…