Category: Integration

Question Number 114135 by mnjuly1970 last updated on 17/Sep/20 $$\dots .\mathcal{A}dvancedmathematics\dots$$$$i::provethat:\mathrm{\Omega }=\frac{1}{\pi }{\int }_0^{\mathrm{\infty }}\frac{1}{{(x^2-x+1)}^2\sqrt{x}}dx=1$$$$ii::evaluate::\mathrm{\Phi }={\int }_0^1{x}^{2}ln\left(x\right)ln(1-x)dx=???$$$$\dots .m.n.july.1970\dots .$$$$\:…

Question Number 114105 by gab last updated on 17/Sep/20 $$\int \frac{arctan\left(e^x\right)}{\sqrt{x}}dx$$ Commented by sherzodbek last updated on 17/Sep/20 salom Terms of Service Privacy…

Question Number 114103 by gab last updated on 17/Sep/20 $$\int \sqrt{ln\left(tan\left(x\right)\right)}dx$$ Commented by MJS_new last updated on 17/Sep/20 $$\mathrm{seems}\mathrm{unsolveable}\mathrm{to}\mathrm{me}$$ Terms of Service…

Question Number 114072 by Lordose last updated on 17/Sep/20 $$\int \frac{1}{\mathbf{sinx}+\mathbf{cosx}}\mathbf{dx}$$ Answered by Olaf last updated on 17/Sep/20 $$x=\frac{\pi }{4}-u$$$$\sin x+\cos x=$$$$\left(\mathrm{sin}\frac{\pi}{\mathrm{4}}\mathrm{cos}{u}−\mathrm{sin}{u}\mathrm{cos}\frac{\pi}{\mathrm{4}}\right)+\left(\mathrm{cos}\frac{\pi}{\mathrm{4}}\mathrm{cos}{u}+\mathrm{sin}\frac{\pi}{\mathrm{4}}\mathrm{sin}{u}\right) \…

Question Number 114044 by Her_Majesty last updated on 16/Sep/20 $$oldandunanswered\dots MrMathdave???$$$$\int x^{2}ln(1-x)ln(1+x)dx=?$$ Answered by mathdave last updated on 17/Sep/20 $$sokution$$$${put}\:{x}=\left(\mathrm{2}{y}−\mathrm{1}\right)\:\:\left({wat}\:{i}\:{did}\:{here}\:{is}\:{logical}\right)…