Category: Integration

Question Number 59161 by maxmathsup by imad last updated on 05/May/19 $$calculatef\left(a\right)={\int }_0^{\mathrm{\infty }}\frac{ln(a^2+x^2)}{a^2+x^2}dxwith>0$$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty}…

Question Number 124672 by sdfg last updated on 05/Dec/20 $${\int }_{-3}^{-2}{(y+3)}^6{(y+2)}^{4}dy$$ Commented by mohammad17 last updated on 05/Dec/20 $${put}:{n}={y}+\mathrm{3}\Rightarrow{y}={n}−\mathrm{3}\Rightarrow{dy}={dn} \…

Question Number 124654 by benjo_mathlover last updated on 05/Dec/20 $$\underset{1/\sqrt{2}}{\stackrel{1/2}{\int }}\frac{e^{{\cos }^{-1}\left(x\right)}}{\sqrt{1-x^2}}dx?$$ Commented by mohammad17 last updated on 05/Dec/20 $$…

Question Number 190172 by jlewis last updated on 29/Mar/23 $$Integrate$$$${\int }_0^1{Sin}^2\left(2\mathrm{\Pi }x\right)dx$$ Answered by mehdee42 last updated on 29/Mar/23 $$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…

Question Number 124632 by liberty last updated on 05/Dec/20 $$Calculate\underset{0}{\stackrel{2}{\int }}\sqrt{\frac{2+x}{2-x}}dx$$ Answered by bemath last updated on 05/Dec/20 $$putx=2\cos 2\theta$$$${I}=\underset{\pi/\mathrm{4}} {\overset{\mathrm{0}}…