Category: Integration

Question Number 63351 by aliesam last updated on 02/Jul/19 Commented by mathmax by abdo last updated on 03/Jul/19 $$letI=\int \frac{dx}{4+{(x-3)}^2}changementx-3=2tgive$$$${I}\:=\:\int\:\:\frac{\mathrm{2}{dt}}{\mathrm{4}+\mathrm{4}{t}^{\mathrm{2}} }\:=\:\int\:\:\:\:\frac{{dt}}{\mathrm{2}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:=\frac{\mathrm{1}}{\mathrm{2}}\:{arctan}\left({t}\right)+{c} \…

Question Number 128851 by mnjuly1970 last updated on 10/Jan/21 $$\dots nicecalculus\left(I\right)\dots$$$$calculate::$$$$$$$$\mathrm{\Psi }={\int }_0^1\{(e-1)\sqrt{log(1+ex-x)}+e^{x^2}\}dx=?$$$$$$ Commented…

Question Number 63292 by aliesam last updated on 02/Jul/19 $${\int }_0^1{\int }_0^1\frac{dy}{1+y(x^2-x)}dx$$ Commented by mathmax by abdo last updated on…

Question Number 63273 by mathmax by abdo last updated on 01/Jul/19 $$letF\left(x\right)={\int }_{x^2}^{x^3}\frac{sin\left(t\right)}{t+x}dt$$$$1)calculate{lim}_{x\to 0}F\left(x\right)and{lim}_{x\to +\mathrm{\infty }}F\left(x\right)$$$$\left.\mathrm{2}\right){calculste}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}^{'} \left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:{F}^{'}…

Question Number 128797 by mnjuly1970 last updated on 10/Jan/21 $$\dots nicecalculus\dots$$$$\varphi \stackrel{???}{=}{\int }_0^{\mathrm{\infty }}\left(\frac{tanh\left(x\right)}{e^x}\right)dx$$$$$$ Answered by Dwaipayan Shikari last…