Category: Integration

Question Number 61978 by maxmathsup by imad last updated on 13/Jun/19 $$letf\left(x\right)={\int }_0^{1}ln(1-{xt}^3)dtwith\mid x\mid <1$$$$1)findaexplicitformoff\left(x\right)$$$$2)calculate{\int }_0^{1}ln(1-\frac{1}{\sqrt{2}}{t}^3)dt$$$$\left.\mathrm{3}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 61976 by maxmathsup by imad last updated on 13/Jun/19 $$let{A}_n={\int }_{\frac{1}{n}}^n\frac{arctan(x^2+y^2)}{x^2+y^2}dxdy$$$$1)calculate{A}_n$$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \…

Question Number 61966 by aliesam last updated on 12/Jun/19 $$\int \frac{1}{e^{2x}-e^{-2x}}dx$$ Commented by kaivan.ahmadi last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} }}{dx}=\int\frac{{e}^{\mathrm{2}{x}} }{{e}^{\mathrm{2}{x}}…

Question Number 127468 by bramlexs22 last updated on 30/Dec/20 $${\int }_0^{\mathrm{\infty }}\frac{{\mathrm{x}}^3\sin \left(\lambda \mathrm{x}\right)}{{\mathrm{x}}^4+4}\mathrm{dx}=?$$ Commented by bramlexs22 last updated on 30/Dec/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:\mathrm{sir} \…

Question Number 61921 by maxmathsup by imad last updated on 11/Jun/19 $$letA={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x+1}{(x^2+x+1)(x^2-2i)}dx$$$$1)calculateA$$$$2)extractRe\left(A\right)andIm\left(A\right)anddetermineitsvalues(i^2=-1)$$ Commented by…