Category: Integration

Question Number 125962 by bramlexs22 last updated on 15/Dec/20 $$\underset{1}{\stackrel{3}{\int }}{x}^{2x}(1+\ln x)dx=?$$ Answered by liberty last updated on 16/Dec/20 $$\:{let}\:{x}^{{x}} \:=\:{r}\:\rightarrow$$\{\begin{array}{l}x=1\to r=1\\ x=3\to r=27\end{array}$$\:\wedge\:{dr}\:=\:{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}…

Question Number 60413 by tanmay last updated on 20/May/19 Commented by Meritguide1234 last updated on 21/May/19 $$\mathrm{why}\mathrm{do}\mathrm{you}\mathrm{post}\mathrm{same}\mathrm{question}\mathrm{and}\mathrm{solition}\mathrm{from}\mathrm{goiit}\mathrm{page}\mathrm{by}\mathrm{Sourav}\mathrm{De}$$ Commented by MJS last updated on…

Question Number 125922 by mnjuly1970 last updated on 15/Dec/20 $$\dots advancedcalculus\dots$$$$evaluate:::\mathrm{\Omega }\stackrel{???}{=}{\int }_0^{\mathrm{\infty }}cos\left(x^2\right)ln\left(x\right)dx$$$$:::::::::$$ Answered by mathmax by abdo…

Question Number 125919 by Eric002 last updated on 15/Dec/20 $${\int }_0^{\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}\frac{dxdydzdt}{{(cosh\left(x\right)+cosh\left(y\right)+cosh\left(z\right)+cosh\left(t\right))}^4}$$$$=\frac{7\zeta \left(3\right)-6}{12}$$ Terms of…

Question Number 125911 by Lordose last updated on 15/Dec/20 $${\int }_0^{\mathrm{\infty }}\frac{\mathrm{xln}(1+\mathrm{x})}{1+{\mathrm{x}}^4}\mathrm{dx}$$ Answered by mathmax by abdo last updated on 15/Dec/20 $$\mathrm{A}\:=\int_{\mathrm{0}}…