Category: Integration

Question Number 140282 by qaz last updated on 06/May/21 $$\underset{k=0}{\sum ^{p-1}}\left(\begin{array}{c}p\\ k\end{array}\right)\sin \left[2(p-k)x\right]=?$$$$\left(\begin{array}{c}p\\ 0\end{array}\right)\sin \left(2px\right)+\left(\begin{array}{c}p\\ 1\end{array}\right)\sin \left[(2p-2)x\right]+\left(\begin{array}{c}p\\ 2\end{array}\right)\sin \left[(2p-4)x\right]+\dots +\left(\begin{array}{c}p\\ p-1\end{array}\right)\sin \left(2x\right)=2^p\cdot \cos {}^p\left(x\right)\cdot \sin \left(px\right)???$$$$or{\int }_0^{\mathrm{\infty }}\frac{\cos {}^p\left(x\right)\cdot \sin \left(px\right)}{x}dx=\frac{\pi }{2}(1-2^{-p})why???$$ Terms…

Question Number 74720 by chess1 last updated on 29/Nov/19 Commented by mathmax by abdo last updated on 29/Nov/19 $$changement\sqrt{\frac{x-1}{x+1}}=tgivex-1=t^2(x+1)\Rightarrow (1-t^2)x=1+t^2\Rightarrow$$$${x}=\frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}}…

Question Number 140221 by qaz last updated on 05/May/21 $${\int }_0^{\mathrm{\infty }}{x}^2[ln(1+e^x)-x]dx=\frac{7{\pi }^4}{360}$$ Answered by Dwaipayan Shikari last updated on 05/May/21…

Question Number 140200 by qaz last updated on 05/May/21 $${\int }_0^{\mathrm{\infty }}{\left(\frac{lnx}{x-1}\right)}^{3}dx={\pi }^2$$ Commented by Ar Brandon last updated on 05/May/21 $$\Phi=\int_{\mathrm{0}} ^{\infty}…

Question Number 140191 by kiinali last updated on 05/May/21 $$\int 3x$$ Terms of Service Privacy Policy Contact: info@tinkutara.com