Category: Integration

Question Number 110218 by 150505R last updated on 27/Aug/20 Answered by 1549442205PVT last updated on 28/Aug/20 $$\mathrm{Let}\mathrm{ABCD}\mathrm{be}\mathrm{trapezum}\mathrm{with}\mathrm{AB}//\mathrm{CD}$$$$\mathrm{Through}\mathrm{the}\mathrm{vertex}\mathrm{A}\mathrm{draw}\mathrm{a}\mathrm{line}\mathrm{d}$$$$\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{diagonal}\mathrm{BD}\mathrm{we}\mathrm{have}$$$$\mathrm{ABDE}(\mathrm{E}=\mathrm{d}\cap \left[\mathrm{CD}\right))\mathrm{is}\mathrm{a}\mathrm{paralelogram}$$$$,\mathrm{so}\:\mathrm{AB}=\mathrm{DE}.\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:\mathrm{we}…

Question Number 44674 by MJS last updated on 03/Oct/18 $$\mathrm{solving}\mathrm{some}\mathrm{integrals}\mathrm{we}\mathrm{might}\mathrm{meet}\mathrm{some}$$$$\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{functions}\mathrm{which}\mathrm{cannot}\mathrm{be}$$$$\mathrm{solved}\mathrm{with}\mathrm{elementar}\mathrm{knowledge}\mathrm{but}\mathrm{tables}$$$$\mathrm{should}\mathrm{exist}\mathrm{somewhere}\mathrm{in}\mathrm{the}\mathrm{depth}\mathrm{of}\mathrm{the}$$$$\mathrm{www}\dots$$$$\mathrm{these}\mathrm{links}\mathrm{might}\mathrm{be}\mathrm{interesting}$$$$$$$$\mathrm{exponential}\:\mathrm{integral} \…

Question Number 44654 by manish00@gmail.com last updated on 02/Oct/18 $$\int \frac{{\mathbf{e}}^{\mathbf{x}}}{1+{\mathbf{x}}^2}\mathbf{dx}=?$$ Commented by maxmathsup by imad last updated on 02/Oct/18 $${changement}\:{x}={tan}\theta\:{give}\:{I}\:=\int\:\:\frac{{e}^{{tan}\theta} }{\mathrm{1}+{tan}^{\mathrm{2}}…

Question Number 175697 by Tawa11 last updated on 05/Sep/22 $${\int }_0^1\frac{{3\mathrm{x}}^3-{\mathrm{x}}^2+2\mathrm{x}-4}{\sqrt{{\mathrm{x}}^2-3\mathrm{x}+2}}\mathrm{dx}$$ Answered by MJS_new last updated on 05/Sep/22 $$\underset{\mathrm{0}}…

Question Number 44604 by arvinddayama01@gmail.com last updated on 02/Oct/18 $$\int {\left[\frac{\mathbf{log}\mathbf{x}-1}{1+{\left(\mathbf{log}\mathbf{x}\right)}^2}\right]}^2\mathbf{dx}=\frac{\mathbf{x}}{{\left(\mathbf{log}\mathbf{x}\right)}^2+1}+\mathbf{C}$$ Commented by prof Abdo imad last updated on 02/Oct/18 $${let}\:\varphi\left({x}\right)=\frac{{x}}{\mathrm{1}+\left({lnx}\right)^{\mathrm{2}}…