Category: Integration

Question Number 160767 by cortano last updated on 06/Dec/21 $${\int }_0^{\frac{\pi }{2}}\frac{\cos {}^2\mathrm{x}}{\cos {}^2\mathrm{x}+4\sin {}^2\mathrm{x}}\mathrm{dx}=?$$ Answered by MJS_new last updated on 06/Dec/21 $$\underset{\mathrm{0}}…

Question Number 95221 by mathmax by abdo last updated on 24/May/20 $$\mathrm{calculate}{\int }_0^{\pi }\ln (2+\cos \theta )\mathrm{d}\theta$$ Answered by mathmax by abdo last updated on 24/May/20…

Question Number 95208 by Ar Brandon last updated on 24/May/20 $$\mathrm{i}\mathrm{\setminus }\int \frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\mathrm{ii}\mathrm{\setminus }\int \frac{\mathrm{cosx}}{\mathrm{x}}\mathrm{dx}$$$$\mathrm{iii}\mathrm{\setminus }\int \frac{1}{\mathrm{lnx}}\mathrm{dx}\mathrm{iv}\mathrm{\setminus }\int \sqrt{1-{\mathrm{k}}^2{\sin }^2\mathrm{x}}\mathrm{dx}$$$$\mathrm{v}\mathrm{\setminus }\int \sqrt{\mathrm{sinx}}\mathrm{dx}\mathrm{vi}\mathrm{\setminus }\int \sin \left({\mathrm{x}}^2\right)\mathrm{dx}$$$$\mathrm{vii}\mathrm{\setminus }\int \cos \left({\mathrm{x}}^2\right)\mathrm{dx}\mathrm{viii}\mathrm{\setminus }\int \mathrm{xtanxdx}$$$$\mathrm{ix}\backslash\:\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\backslash\int\mathrm{e}^{\mathrm{x}^{\mathrm{2}}…

Question Number 95198 by Fikret last updated on 23/May/20 $$\int \sqrt{\frac{x+2}{x-3}}dx=?$$ Answered by MJS last updated on 23/May/20 $$\int \sqrt{\frac{x+2}{x-3}}dx=$$$$[t=\sqrt{\frac{x+2}{x-3}}\to dx=-\frac{2}{5}\sqrt{{(x-3)}^3(x+2)}]$$$$=−\mathrm{10}\int\frac{{t}^{\mathrm{2}}…

Question Number 160734 by mnjuly1970 last updated on 05/Dec/21 $$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{\Phi }={\int }_0^1{\left(\frac{{ln}^{}\left(\frac{1}{1-x}\right)}{x}\right)}^{3}dx\stackrel{?}{=}3(\zeta \left(2\right)+\zeta \left(3\right))$$$$----solution----$$$$\:\:\:\:\:\:\:\:\Phi\:\overset{\mathrm{I}.\mathrm{B}.\mathrm{P}} {=}\:\left[\:\frac{\:\mathrm{1}}{\mathrm{2}{x}^{\:\mathrm{2}} }\:{ln}^{\:\mathrm{3}}…