Category: Integration

Question Number 17444 by Tinkutara last updated on 06/Jul/17 $$\mathrm{Evaluate}:\underset{0}{\stackrel{\frac{\pi }{4}}{\int }}\frac{dx}{{\cos }^{3}x\sqrt{2\sin 2x}}$$ Answered by Arnab Maiti last updated on 10/Jul/17 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…

Question Number 82972 by mathmax by abdo last updated on 26/Feb/20 $$calculate{\int }_0^{1}arctan\left(x\right)ln(1+x)dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 82971 by mathmax by abdo last updated on 26/Feb/20 $$1)find\int \frac{dx}{{(x^2+x+1)}^6}$$$$2)calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dx}{{(x^2+x+1)}^6}$$ Commented by mathmax…

Question Number 148467 by bramlexs22 last updated on 28/Jul/21 Answered by puissant last updated on 28/Jul/21 $$\mathrm{x}=\tan \left(\mathrm{t}\right)\Rightarrow \mathrm{dx}=1+{\tan }^2\left(\mathrm{t}\right)\mathrm{dt}$$$$0⩽\mathrm{x}⩽\mathrm{\infty }\Rightarrow 0⩽\mathrm{t}⩽\frac{\pi }{2}$$$$\Rightarrow\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{arctan}\left(\mathrm{tan}\left(\mathrm{t}\right)\right)}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \left(\mathrm{t}\right)}\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}}…

Question Number 17377 by tawa tawa last updated on 04/Jul/17 $$\int \frac{\cos \left(\mathrm{x}\right)}{2-\cos \left(\mathrm{x}\right)}\mathrm{dx}$$ Answered by ajfour last updated on 05/Jul/17 $$\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{x}/\mathrm{2}\right)}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}/\mathrm{2}\right)}\:=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }…