Category: Integration

Question Number 32705 by caravan msup abdo. last updated on 31/Mar/18 $$letgivef\left(x\right)={\int }_0^{\mathrm{\infty }}ln(1+\frac{x}{t^2})dtwith\mid x\mid <1$$$$findasimpleformoff\left(x\right).$$ Commented by abdo imad last updated…

Question Number 163759 by amin96 last updated on 10/Jan/22 $${\int }_0^1{\left(\frac{\mathbf{ln}(1+\mathbf{x})}{\mathbf{x}}\right)}^2\mathbf{dx}=?$$$$\mathbf{by}\mathbf{M}.\mathbf{A}$$ Answered by Kamel last updated on 10/Jan/22 $$\Omega\overset{{IBP}}…

Question Number 163751 by amin96 last updated on 10/Jan/22 $${\int }_0^1\mathit{l}\mathit{n}(1+\mathit{x})\mathit{l}\mathit{n}(1-\mathit{x})\mathit{d}\mathit{x}=?$$$$\mathit{b}\mathit{y}\mathit{M}\mathit{A}\mathit{T}\mathit{H}.\mathit{A}\mathit{M}\mathit{I}\mathit{N}$$$$--------------------$$ Answered by Kamel last updated on 10/Jan/22…

Question Number 98182 by abdomathmax last updated on 12/Jun/20 $$\mathrm{find}\int {\mathrm{x}}^2\sqrt{\frac{2-\mathrm{x}}{2+\mathrm{x}}}\mathrm{dx}$$ Answered by MJS last updated on 12/Jun/20 $$\int x^2\sqrt{\frac{2-x}{2+x}}dx=$$$$\:\:\:\:\:\left[{t}=\sqrt{\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}}\:\rightarrow\:{dx}=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\left(\mathrm{2}+{x}\right)\left(\mathrm{2}−{x}\right)^{\mathrm{3}} }{dt}\right]…

Question Number 98179 by abdomathmax last updated on 12/Jun/20 $$\mathrm{calculate}{\int }_1^{+\mathrm{\infty }}\frac{\mathrm{dx}}{{\mathrm{x}}^2{(1-{\mathrm{x}}^2)}^3}$$ Answered by MJS last updated on 12/Jun/20 $$\mathrm{I}\:\mathrm{love}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}……