Category: Integration

Question Number 74799 by mathmax by abdo last updated on 30/Nov/19 $$provethat0⩽{\int }_0^{\mathrm{\infty }}\frac{t^2{e}^{-nt}}{e^t-1}dt⩽\frac{1}{n^2}fornintegrnot0$$ Answered by mind is power…

Question Number 140334 by mnjuly1970 last updated on 06/May/21 $$$$$$calculate::$$$$\mathit{\xi }:={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}ln(2-2cos\left(x^2\right))dx=?$$$$$$ Answered by ArielVyny last…

Question Number 140330 by Satyendra last updated on 06/May/21 $$FindtheIntegrationValue:$$$$1\int \frac{\sqrt{x}d\left(x\right)}{1{+}^3\sqrt{x}}=?$$$$2\int \frac{dx}{x^{\frac{1}{2}}-x^{\frac{1}{4}}}=?$$ Answered by john_santu last…

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}}…