Category: Integration

Question Number 132070 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{I}=\int \frac{\mathrm{x}}{{({\mathrm{x}}^4-1)}^2}\mathrm{dx}?$$ Answered by liberty last updated on 10/Feb/21 $$\mathrm{I}=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} \right)}{\left(\left(\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}}…

Question Number 66517 by mhmd last updated on 16/Aug/19 $$findtheareacos\left(2\theta \right)$$ Commented by MJS last updated on 16/Aug/19 $$\mathrm{you}\mathrm{must}\mathrm{give}\mathrm{borders}\dots$$ Answered by Smail…

Question Number 949 by 123456 last updated on 04/May/15 $$f:\mathbb{N}\to \mathbb{R}$$$$g:\mathbb{N}\to \mathbb{R}$$$$f\left(n\right)=\underset{0}{\stackrel{2\pi }{\int }}{x}^n\sin xdx$$$$g\left(n\right)=\underset{0}{\stackrel{2\pi }{\int }}{x}^n\cos xdx$$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \…

Question Number 66483 by ~ À ® @ 237 ~ last updated on 16/Aug/19 $$calculate\underset{k=2}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^k}{k}\zeta \left(k\right)if\zeta \left(s\right)=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^s}$$ Commented by…

Question Number 66476 by aliesam last updated on 15/Aug/19 Commented by kaivan.ahmadi last updated on 15/Aug/19 $$t=4x+1\Rightarrow$$$$\frac{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow\frac{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{t}}+\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow \…