Category: Integration

Question Number 39336 by rahul 19 last updated on 05/Jul/18 Commented by ajfour last updated on 05/Jul/18 $$-2isevenorodd?$$ Commented by rahul 19 last…

Question Number 170388 by infinityaction last updated on 22/May/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 170384 by amin96 last updated on 22/May/22 $$\mathbf{Prove}\mathbf{that}$$$${\int }_0^{\frac{\pi }{2}}\mathbf{ln}(\mathbf{a}-{\mathbf{sin}}^2\left(\mathbf{x}\right))\mathbf{dx}=\pi \mathbf{ln}(\sqrt{\frac{\mathbf{a}-1}{\mathbf{a}}}+1)+\frac{\pi }{2}\mathbf{ln}\left(\frac{\mathbf{a}}{4}\right)$$$$\mathbf{a}>0\mathbf{I}\mathit{m}\left\{\mathit{a}\right\}\ne 0$$ Terms of Service Privacy Policy Contact:…

Question Number 39292 by math khazana by abdo last updated on 04/Jul/18 $$letf\left(x\right)=arctan\left(2x\right)$$$$1)calculate{f}^{\left(n\right)}\left(x\right)then{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie$$$$3)letF\left(t\right)={\int }_0^{t}arctan\left(2x\right)dx$$$${developp}\:{F}\:{at}\:{integr}\:{serie}…

Question Number 170349 by antoineop last updated on 21/May/22 $$$$$$helpplease$$$${\stackrel{\mathrm{\infty }}{\int }}_1(\frac{1}{t}-{\sin }^{-1}\left(\frac{1}{t}\right))dt$$$$Icanshowthatitisequalto$$$$−\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{{n}} \frac{\left(\mathrm{2}{n}−\mathrm{1}\right)!}{\mathrm{4}^{{n}} \left({n}!\right)^{\mathrm{2}} \left(\mathrm{2}{n}+\mathrm{1}\right)}…