Category: Integration

Question Number 96652 by bobhans last updated on 03/Jun/20 $$\int \frac{x\cos x-\sin x}{x^2+\sin {}^{2}x}dx$$ Answered by bemath last updated on 03/Jun/20 $$\int\:\frac{\left(\frac{\mathrm{cos}\:{x}}{{x}}−\frac{\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} }\right)\:{dx}}{\mathrm{1}+\left(\frac{\mathrm{sin}\:{x}}{{x}}\right)^{\mathrm{2}} }\:=\mathrm{I} \…

Question Number 162177 by mnjuly1970 last updated on 27/Dec/21 $$$$$$\mathit{\varphi }={\int }_0^1\frac{{\ln }^2\left(x\right).{\mathrm{Li}}_2\left(x\right)}{x^{}}dx=?$$ Answered by Ar Brandon last updated…

Question Number 31106 by abdo imad last updated on 02/Mar/18 $$provethat{\int }_0^{\mathrm{\infty }}{e}^{-x^2}={lim}_{n\to +\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}\frac{dx}{{(1+x^2)}^n}.$$$$2)provethat\frac{1}{\sqrt{\pi }}={lim}_{n\to \mathrm{\infty }}\frac{1.3.5\dots .(2n-3)}{2.4.6\dots .(2n-2)}\sqrt{n}$$$$\left({wallis}\:{formula}\right).…

Question Number 31103 by abdo imad last updated on 02/Mar/18 $$find{\int }_0^{\mathrm{\infty }}{e}^{-{(x-\frac{a}{x})}^2}dxwitha⩾0.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 31101 by abdo imad last updated on 02/Mar/18 $$letgivef\left(x\right)={\int }_0^x{t}^2{e}^{-2t^2}sin\left(2(x-t)\right)dtcalculate$$$$f^{{}^{″}}+4fthenfinff\left(x\right).$$ Terms of Service Privacy…