Category: Integration

Question Number 190692 by mnjuly1970 last updated on 09/Apr/23 $$$$$$\mathrm{calculate}$$$$$$$$\mathit{\varphi }={\int }_0^{\mathrm{\infty }}\frac{{\sin }^3\left(x\right)\ln \left(x\right)}{x}\mathrm{d}x=?$$$$$$$$@\mathrm{nice}-\mathrm{mathematics}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…

Question Number 125133 by mnjuly1970 last updated on 08/Dec/20 $$\dots ◂advancedcalculus▸\dots$$$$provethat:::$$$$\mathrm{\Omega }={\int }_0^1\left\{\frac{cos\left(log\left(x\right)\right)-1}{log\left(x\right)}\right\}dx=\frac{log\left(2\right)}{2}$$$$\dots \ast adoptedfromyoutube\ast \dots$$$$\ast \ast youtubesolutionisnotconsidered\ast \ast$$$$$$ Answered…

Question Number 125114 by bramlexs22 last updated on 08/Dec/20 $$solve\int \frac{dx}{{(x^3-1)}^2}?$$ Commented by liberty last updated on 08/Dec/20 $${Ostrogradsky}^{\prime }smethod\left(ProfsirMJS\right)$$ Answered…

Question Number 59575 by maxmathsup by imad last updated on 12/May/19 $$find\int \frac{sin\left(2x\right)}{1+{cos}^{2}x}dx$$ Answered by Smail last updated on 12/May/19 $$\int\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx}=\int\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\frac{\mathrm{1}+{cos}\mathrm{2}{x}}{\mathrm{2}}}{dx} \…

Question Number 125098 by mnjuly1970 last updated on 08/Dec/20 $$\dots nicecalculus\dots$$$$provethat::{Apery}^{\prime }sconstant$$$$\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} {x}^{\mathrm{2}^{\mathrm{2}} } +\mathrm{4}^{\mathrm{3}} {x}^{\mathrm{2}^{\mathrm{3}} } +…\right)\frac{{ln}^{\mathrm{2}} \left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}\right\}{dx} \…