Category: Integration

Question Number 95692 by mathmax by abdo last updated on 27/May/20 $$\mathrm{calculate}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{\mathrm{xsin}\left(2\mathrm{x}\right)}{{({\mathrm{x}}^2+\mathrm{x}+1)}^2}\mathrm{dx}$$ Answered by mathmax by abdo last updated…

Question Number 161212 by cortano last updated on 14/Dec/21 $${\int }_0^{\frac{\pi }{2}}\frac{x\sin x\cos x}{\cos {}^{4}x+\sin {}^{4}x}dx=?$$ Commented by puissant last updated on 15/Dec/21 Commented by…

Question Number 95673 by Rio Michael last updated on 26/May/20 $${\int }_0^1\frac{1}{\sqrt{3+4x-4x^2}}dx=?$$ Commented by Tony Lin last updated on 26/May/20 $$\int_{\mathrm{0}}…

Question Number 95650 by  M±th+et+s last updated on 26/May/20 $${\int }_0^1\left\{{(-1)}^{\lfloor \frac{1}{x}\rfloor }\frac{1}{x}\right\}dx$$$$\{..\}isfractionalpart$$$$\lfloor ..\rfloor isfloorfunction$$ Answered by mathmax by abdo last…

Question Number 161178 by amin96 last updated on 13/Dec/21 $${\underset{2}{\int }}^{\mathrm{\infty }}\frac{\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\left(\mathit{x}\right)}{\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\left(\frac{\mathit{x}}{2}\right)}\mathit{d}\mathit{x}=???$$ Answered by MJS_new last updated on 13/Dec/21 $$1<\frac{\arctan x}{\arctan \frac{x}{2}}⩽2$$$$\Rightarrow \…