Category: Integration

Question Number 135737 by Ar Brandon last updated on 15/Mar/21 $${\int }_{-2\pi }^{4\pi }\frac{3}{5-4\mathrm{cosx}}\mathrm{dx}$$ Answered by mathmax by abdo last updated on 15/Mar/21 $$\Phi=\int_{−\mathrm{2}\pi}…

Question Number 135693 by liberty last updated on 15/Mar/21 $$\mathrm{\Omega }=\int \frac{x-1}{(x-2){(x^2-2x+2)}^2}dx$$ Answered by MJS_new last updated on 15/Mar/21 $$\int\frac{{x}−\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx}= \…

Question Number 135673 by liberty last updated on 14/Mar/21 $$\int \frac{x^2+1}{x^4+x^2+1}dx$$ Answered by Olaf last updated on 15/Mar/21 $$\Omega\:=\:\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}}…

Question Number 4575 by FilupSmith last updated on 08/Feb/16 $${\int }_a^{\mathrm{\infty }}\frac{1}{x}dx=\mathrm{\infty }$$$$$$$${\int }_a^{\mathrm{\infty }}\lfloor \frac{1}{x}\rfloor dx=S$$$$a>0$$$$$$$$\mathrm{Is}\:{S}\:\mathrm{finite}?\:\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{for}\:{S}? \…

Question Number 135633 by metamorfose last updated on 14/Mar/21 $$\int \frac{1}{x^{\frac{1}{3}}+1}dx=\dots ?$$ Answered by Ñï= last updated on 14/Mar/21 $$\int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}}\overset{{t}={x}^{\frac{\mathrm{1}}{\mathrm{3}}} } {=}\int\frac{\mathrm{3}{t}^{\mathrm{2}} {dt}}{{t}+\mathrm{1}}=\mathrm{3}\int\frac{\left({t}+\mathrm{1}\right)\left({t}−\mathrm{1}\right)+\mathrm{1}}{{t}+\mathrm{1}}{dt}=\mathrm{3}\int\left\{\left({t}−\mathrm{1}\right)+\frac{\mathrm{1}}{{t}+\mathrm{1}}\right\}{dt}…