Category: Integration

Question Number 67799 by mathmax by abdo last updated on 31/Aug/19 $$calculate{\int }_0^{\mathrm{\infty }}\frac{dx}{(x^2-e^{ia})(x^2-e^{ib})}witha>0andb>0$$ Commented by MJS last updated…

Question Number 133305 by liberty last updated on 21/Feb/21 $${\int }_0^{2\pi }\frac{\mathrm{dx}}{5+3\sin 2\mathrm{x}}=?$$ Answered by physicstutes last updated on 21/Feb/21 $$\mathrm{set}t=\tan x$$$$\Rightarrow\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:=\:\frac{\mathrm{2}\:\mathrm{tan}\:{x}}{\mathrm{1}+\:\mathrm{tan}^{\mathrm{2}} {x}}\:\:=\:\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…

Question Number 133291 by liberty last updated on 21/Feb/21 $$\int \frac{{\left({\mathrm{x}}^4\right)}^2}{{(1+{\mathrm{x}}^6)}^2}\mathrm{dx}=?$$ Answered by EDWIN88 last updated on 21/Feb/21 $$\mathrm{integration}\:\mathrm{by}\:\mathrm{parts} \…

Question Number 67744 by mathmax by abdo last updated on 31/Aug/19 $$letf\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{sin\left(t^2\right)}{{(x^2+t^2)}^2}dtwithx>0$$$$1)determineaexplicitformforf\left(x\right)$$$$\left.\mathrm{2}\right)\:{find}\:\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}}…

Question Number 2186 by Yozzi last updated on 07/Nov/15 $$LetJ={\int }_0^{\mathrm{\infty }}f\left({(x-x^{-1})}^2\right)dxwherefis$$$$anyfunctionforwhichtheintegral$$$$exists.Showthat$$$${J}=\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{2}} {f}\left(\left({x}−{x}^{−\mathrm{1}} \right)^{\mathrm{2}} \right){dx}=\mathrm{0}.\mathrm{5}\int_{\mathrm{0}}…