Category: Integration

Question Number 193214 by Humble last updated on 07/Jun/23 $$Evaluate$$$$\mathrm{\Omega }={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{e^{\frac{x}{2}}ln\left(\sqrt{\frac{3-x}{3+x}}\right)}{{tanh}^{-1}\left(\frac{x}{3}\right)(1+e^x)}dx$$ Terms of Service Privacy Policy Contact:…

Question Number 131068 by EDWIN88 last updated on 01/Feb/21 $$\int \sin {}^{2}x\cos 4xdx=?$$ Answered by Ar Brandon last updated on 01/Feb/21 $$\mathcal{I}=\int {\sin }^2\mathrm{xcos}4\mathrm{xdx}=\frac{1}{2}\int (1+\cos 2\mathrm{x})\cos 4\mathrm{xdx}$$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int\left[\mathrm{cos4x}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos6x}+\mathrm{cos2x}\right)\right]\mathrm{dx}…

Question Number 131053 by pipin last updated on 01/Feb/21 $$\int \frac{{\mathrm{x}}^2+2}{{\mathrm{x}}^4+4}\mathrm{dx}$$ Answered by Ar Brandon last updated on 01/Feb/21 $$\mathcal{I}=\int\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\mathrm{dx}=\int\frac{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}}…

Question Number 131049 by mathmax by abdo last updated on 31/Jan/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\int }_0^{\mathrm{\infty }}\frac{\cos \left(\mathrm{xt}\right)}{{\mathrm{x}}^2+{\mathrm{t}}^2}\mathrm{dt}\mathrm{calculate}{\int }_0^1\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$ Answered by mindispower last updated…

Question Number 65485 by aliesam last updated on 30/Jul/19 $$\int e^{{cos}^{-1}\left(x\right)}dx$$ Answered by MJS last updated on 31/Jul/19 $$\int {\mathrm{e}}^{\arccos x}dx=$$$$\:\:\:\:\:\left[{t}=\mathrm{arccos}\:{x}\:\rightarrow\:{dx}=−\mathrm{sin}\:{t}\:{dt}\right]…