Category: Integration

Question Number 38199 by prof Abdo imad last updated on 22/Jun/18 $$calculate{\int }_0^1\frac{\sqrt{x}}{1+x^2}dx.$$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18 $${x}={t}^{\mathrm{2}\:}…

Question Number 38198 by maxmathsup by imad last updated on 22/Jun/18 $$wegive{\int }_0^{\mathrm{\infty }}{e}^{-x}ln\left(x\right)dx=-\gamma$$$$1)calculatef\left(a\right)={\int }_0^{\mathrm{\infty }}{e}^{-ax}ln\left(x\right)dxwitha>0$$$$\left.\mathrm{2}\right)\:{let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}}…

Question Number 103721 by Dwaipayan Shikari last updated on 16/Jul/20 $${\int }_0^{\mathrm{\infty }}\frac{cosx}{x^2+1}dx$$ Answered by Ar Brandon last updated on 16/Jul/20 $$\mathcal{I}=\int_{\mathrm{0}}…

Question Number 103723 by Ar Brandon last updated on 16/Jul/20 $$\mathrm{Solve}\mathrm{for}\mathrm{n},\mathrm{such}\mathrm{that};$$$$1-\frac{1}{2}+\cdot \cdot \cdot +\frac{{(-1)}^{\mathrm{n}}}{\mathrm{n}+1}={\int }_0^1\frac{{\mathrm{x}}^{\mathrm{n}+1}}{1+\mathrm{x}}\mathrm{dx}-\ln 2-{(-1)}^{\mathrm{n}+1}$$ Terms of Service Privacy Policy Contact:…

Question Number 169230 by Giantyusuf last updated on 26/Apr/22 Answered by Mathspace last updated on 26/Apr/22 $$I{=}_{x=3^{\frac{1}{4}}t}\int \frac{\sqrt{3}{t}^2}{3(1+t^4)}{3}^{\frac{1}{4}}dt$$$$=\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}} \:\int\:\:\frac{{t}^{\mathrm{2}}…