Category: Integration

Question Number 63892 by mathmax by abdo last updated on 10/Jul/19 $$calculateA={\int }_0^{\mathrm{\infty }}\frac{x^{2017}}{1+x^{2019}}dxandB={\int }_0^{\mathrm{\infty }}\frac{x^{2019}}{1+x^{2021}}dx$$$$calculatethefraction\frac{A}{B}$$ Commented…

Question Number 63883 by mmkkmm000m last updated on 10/Jul/19 $$\int ln\left(x\right)ln(1-x)ln(1-2x)dx$$ Commented by mathmax by abdo last updated on 12/Jul/19 $$letA=\int ln\left(x\right)ln(1-x)ln(1-2x)dxwehave$$$${ln}^{'} \left(\mathrm{1}−{u}\right)\:=−\frac{\mathrm{1}}{\mathrm{1}−{u}}\:=−\sum_{{n}=\mathrm{0}}…

Question Number 63852 by aliesam last updated on 10/Jul/19 $$provethat$$$$$$$${\int }_0^{1}arctan\left(x\right)cot\left(\frac{\pi x}{2}\right)dx=\frac{3{ln}^2\left(2\right)}{2\pi }+\frac{ln\pi ln2}{\pi }+{\int }_0^{\mathrm{\infty }}\frac{ln(1+x^2)}{e^{2\pi x}+1}dx$$ Terms of…

Question Number 129377 by pipin last updated on 15/Jan/21 $$\int \frac{\sqrt{\mathbf{x}}}{\sqrt{\mathbf{x}-1}}\mathrm{dx}=\dots$$ Answered by Ar Brandon last updated on 15/Jan/21 $$\mathcal{I}=\int \frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}-1}}\mathrm{dx},\mathrm{x}={\mathrm{t}}^2\Rightarrow \mathrm{dx}=2\mathrm{tdt}$$$$\:\:\:=\mathrm{2}\int\frac{\mathrm{t}^{\mathrm{2}} }{\:\sqrt{\mathrm{t}^{\mathrm{2}}…

Question Number 63822 by mathmax by abdo last updated on 09/Jul/19 $$find\int (x^2+1)\sqrt{\frac{x+1}{x-2}}dx$$ Commented by mathmax by abdo last updated on 11/Jul/19 $${let}\:{A}\:=\int\:\left({x}^{\mathrm{2}}…