Category: Integration

Question Number 58220 by maxmathsup by imad last updated on 20/Apr/19 $$find\int \frac{dx}{(x^2+x)\sqrt{-x^2+2x+3}}$$$$$$ Answered by tanmay last updated on 20/Apr/19…

Question Number 123745 by mnjuly1970 last updated on 27/Nov/20 $$\dots advancedcalculus\dots$$$$evaluationof:$$$$\mathrm{\Omega }={\int }_0^{\frac{\pi }{2}}sin\left(x\right)log\left(sin\left(x\right)\right)dx$$$$byusingtheeulerbetaandgammafunction:$$$$\beta (p,\frac{1}{2})=2{\int }_0^{\frac{\pi }{2}}{sin}^{2p-1}\left(x\right)dx$$$$\:\:\:\frac{{d}\beta\left({p},\frac{\mathrm{1}}{\mathrm{2}}\right)}{{dp}}\:=\mathrm{2}\int_{\mathrm{0}}…

Question Number 58187 by maxmathsup by imad last updated on 19/Apr/19 $$letf\left(x\right)={\int }_1^{3}arctan(x+\frac{x}{t})dtwithx>0$$$$1)determineaexplicitformoff\left(x\right)$$$$2)give{f}^{{}^{\prime }}\left(x\right)atformofintegralandfinditsvalue$$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{arctan}\left(\mathrm{1}+\frac{\mathrm{1}}{{t}}\right){dt}\:\:\:{and}\:\:\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:{arctan}\left(\mathrm{2}+\frac{\mathrm{2}}{{t}}\right){dt}\:.…

Question Number 58184 by maxmathsup by imad last updated on 19/Apr/19 $$find\int \frac{xdx}{sinx+cos\left(2x\right)}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 123710 by Bird last updated on 27/Nov/20 $$calculate{\int }_1^{\sqrt{3}}\frac{dx}{{(x^2+1)}^2{(x+2)}^5}$$ Answered by MJS_new last updated on 27/Nov/20 $$\mathrm{Ostrogradski}\:\mathrm{gives}…