Category: Integration

Question Number 39037 by maxmathsup by imad last updated on 01/Jul/18 $$calculateF\left(x\right)={\int }_0^{2\pi }\frac{cos\left(4t\right)}{x^2-2xcost+1}dt$$ Commented by math khazana by abdo last updated…

Question Number 39035 by maxmathsup by imad last updated on 01/Jul/18 $$findf\left(t\right)={\int }_0^{\mathrm{\infty }}sin\left(x\right)e^{-t\left[x\right]}dxwitht>0$$ Commented by maxmathsup by imad last updated on…

Question Number 39029 by MJS last updated on 01/Jul/18 $$\int \sqrt[3]{3-5\sqrt{1-\frac{1}{x}}}dx=?$$$$\int \frac{1}{\sqrt[3]{3-5\sqrt{1-\frac{1}{x}}}}dx=?$$ Answered by MJS last updated on 02/Jul/18 $$\int \sqrt[3]{3-5\sqrt{1-\frac{1}{x}}}dx=$$$$\:\:\:\:\:\left[{t}=−\mathrm{3}+\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}\:\rightarrow\:{dx}=\frac{\mathrm{2}}{\mathrm{5}}{x}^{\mathrm{2}} \sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}{dt}\right]…

Question Number 39025 by maxmathsup by imad last updated on 01/Jul/18 $$letf\left(x\right)=\frac{cos\left(\alpha x\right)}{cosx}\left(2\pi periodiceven\right)$$$$developpfatfourierserie.$$ Commented by math khazana by abdo last updated on…

Question Number 39024 by maxmathsup by imad last updated on 01/Jul/18 $$findthevalueofI={\int }_0^1\frac{arctan\left(2x\right)}{\sqrt{1+4x^2}}dx$$ Commented by math khazana by abdo last updated…