Category: Integration

Question Number 54585 by peter frank last updated on 07/Feb/19 $$showthat{\int }_0^{\mathrm{\infty }}\frac{x}{1+x^6}dx=\frac{\pi }{3\sqrt{3}}$$$$$$ Commented by maxmathsup by imad last updated…

Question Number 120109 by mnjuly1970 last updated on 29/Oct/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 54556 by gunawan last updated on 06/Feb/19 $${\int }_{-2{\pi }^2}^{2{\pi }^2}\frac{\sin \left(x^2\right)}{x^2}dx$$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Feb/19…

Question Number 54529 by tarun kunar last updated on 05/Feb/19 $$\int 5\cos x-4\sin x/2\cos x+\sin xdx$$ Commented by maxmathsup by imad last updated on 05/Feb/19 $$letI=\int \frac{5cosx-4sinx}{2cosx+sinx}dxletusethechangementtan\left(\frac{x}{2}\right)=t\Rightarrow$$$${I}\:=\int\:\:\frac{\frac{\mathrm{5}\left(\mathrm{1}−{t}^{\mathrm{2}}…

Question Number 120059 by A8;15: last updated on 29/Oct/20 Answered by Lordose last updated on 29/Oct/20 $$$$$$\mathrm{Firstly},\mathrm{compute}\mathrm{the}\mathrm{indefinite}\mathrm{integral}$$$$\mathrm{I}=\int \mathrm{xsec}\left(2\mathrm{x}\right)\mathrm{dx}=\frac{1}{4}\int \mathrm{asec}\left(\mathrm{a}\right)\mathrm{da}\{\mathrm{a}=2\mathrm{x}\}$$$$\mathrm{I}=\frac{1}{4}(\mathrm{alntan}(\frac{\mathrm{a}}{2}+\frac{\pi }{4})-\int \mathrm{lntan}(\frac{\mathrm{a}}{2}+\frac{\pi }{4})\mathrm{da})\left\{\mathrm{IBP}\right\}$$$$\mathrm{set}\:\frac{\mathrm{a}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\:=\:\mathrm{y}\:\Rightarrow\:\mathrm{da}=\mathrm{2dy}…