Category: Integration

Question Number 145339 by qaz last updated on 04/Jul/21 $$\mathrm{Let}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{e}}^{\mathrm{x}}\cos \mathrm{x},\mathrm{Find}\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)}{2^{\mathrm{n}}}=?$$ Answered by mathmax by abdo last updated on…

Question Number 14243 by tawa tawa last updated on 30/May/17 $$\int \left[\mathrm{x}{\left(\mathrm{lnx}\right)}^2\right]\mathrm{dx}$$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/May/17 $${I}=\int{x}^{\mathrm{2}} {ln}^{\mathrm{2}} {xdx} \…

Question Number 79758 by mathmax by abdo last updated on 27/Jan/20 $$findvalueof{\int }_0^{1}ln(1+{ix}^2)dxand{\int }_0^{1}ln(1-{ix}^2)dxwithi=\sqrt{-1}$$ Commented by mathmax by abdo…

Question Number 79730 by Henri Boucatchou last updated on 27/Jan/20 $$I)Forwitchvalueof\alpha theintegral$$$$C={\int }_0^{\mathrm{\infty }}(\frac{1}{\sqrt{1+2x^2}}-\frac{1}{x+1})dxconveege?$$$$Andinthiscasecalculate\alpha .$$$$II)Let\mathrm{\Delta }=\{(x;y)/\mid x\mid +\mid y\mid ⩽2\}$$$$\left.\:\:\:\:\:{a}\right)\:{Calculate}\:{I}_{\mathrm{1}} =\:\int\int_{\Delta} {dxdy}\:\:\:{and}\:\:\int\int_{\Delta} \frac{{dxdy}}{\left(\mid{x}\mid+\mid{y}\mid\right)^{\mathrm{2}}…

Question Number 14181 by tawa tawa last updated on 29/May/17 $$\int {\sec }^6\left(\mathrm{x}\right)\mathrm{dx}$$ Answered by ajfour last updated on 29/May/17 $$let\tan x=t$$$$\Rightarrow\mathrm{sec}\:^{\mathrm{2}} {xdx}={dt},\:{and}\:{we}\:{know}…