Category: Integration

Question Number 57235 by maxmathsup by imad last updated on 31/Mar/19 $$calculate{\int }_0^{\frac{\pi }{2}}\frac{cosx-sinx}{\sqrt{{cos}^{8}x+{sin}^{8}x}}dx$$ Commented by maxmathsup by imad last updated…

Question Number 57231 by maxmathsup by imad last updated on 31/Mar/19 $$findtbevalueof{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x-3}{(x^2+1){(x^2-x+2)}^2}dx$$ Commented by maxmathsup by imad last…

Question Number 57228 by maxmathsup by imad last updated on 31/Mar/19 $$findf\left(x\right)={\int }_1^2\frac{ln(1+xt)}{t^2}dtwithx>0$$ Commented by maxmathsup by imad last updated on…

Question Number 57227 by maxmathsup by imad last updated on 31/Mar/19 $$letf\left(\alpha \right)={\int }_0^1\frac{arctan\left(\alpha x\right)}{1+\alpha x^2}dxwith\alpha real$$$$1)findf\left(\alpha \right)intermsof\alpha$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctan}\left(\mathrm{4}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }{dx}…

Question Number 57225 by maxmathsup by imad last updated on 31/Mar/19 $$1)calculatef\left(a\right)={\int }_0^a\frac{2x-1}{(x^2-x+3)(x^2+1)}dx$$$$1)calculatef\left(1\right)andf\left(2\right)$$ Commented by maxmathsup by imad…