Category: Integration

Question Number 122290 by mnjuly1970 last updated on 15/Nov/20 $$\dots nicecalculus\dots$$$$calculate::$$$$\mathrm{\Omega }={\int }_0^1{x}^2(\psi (1+x)-\psi (2-x))dx=???$$$$.m.n.1970.$$ Commented by Dwaipayan Shikari…

Question Number 122274 by benjo_mathlover last updated on 15/Nov/20 $$\int \frac{\sqrt{1-\sqrt{x}}}{\sqrt{1+\sqrt{x}}}dx?$$ Answered by liberty last updated on 15/Nov/20 $$\mathrm{let}\sqrt{\mathrm{x}}=\cos \theta \Rightarrow \mathrm{x}=\cos {}^2\theta$$$$\Rightarrow \mathrm{dx}=-2\sin \theta \cos \theta \mathrm{d}\theta$$$$\mathrm{I}\:=\int\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\theta}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:\theta}}\:\left(−\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:\right)\mathrm{d}\theta…

Question Number 56699 by maxmathsup by imad last updated on 21/Mar/19 $$let{f}_n\left(a\right)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{sin\left(x^n\right)}{x^2+a^2}dxwithapositifrealnot0andnfromN$$$$1)findaexplicitformoff\left(a\right)$$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({x}^{{n}}…

Question Number 122205 by mathmax by abdo last updated on 14/Nov/20 $$\mathrm{find}\int \frac{\mathrm{dx}}{\mathrm{x}(\mathrm{x}+1)\sqrt{{\mathrm{x}}^2+\mathrm{x}}}$$ Commented by liberty last updated on 15/Nov/20 $$\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}}…

Question Number 187700 by cortano12 last updated on 20/Feb/23 $$Findminimumareaofthepart$$$$y=x^{2}andy=kx(x^2-k),k>0$$ Commented by cortano12 last updated on 21/Feb/23 Terms of…