Category: Integration

Question Number 118834 by bramlexs22 last updated on 20/Oct/20 $$\int \frac{x^4+1}{x^5+4x^3}dx$$ Answered by bobhans last updated on 20/Oct/20 $$\:{Solve}\:\int\:\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{4}{x}^{\mathrm{3}}…

Question Number 53293 by gunawan last updated on 20/Jan/19 $${\int }_{-1/2}^{1/2}\mid x\cos \frac{\pi x}{2}\mid dx=\dots$$ Commented by maxmathsup by imad last updated on 20/Jan/19 $${we}\:{have}\:{f}\left({x}\right)=\mid{xcos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid=\mid{x}\mid\mid{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\mid\:{is}\:{a}\:{even}\:{function}\:{so} \…

Question Number 53292 by gunawan last updated on 20/Jan/19 $${\int }_0^1{e}^{x^2}dx=..$$ Commented by maxmathsup by imad last updated on 20/Jan/19…

Question Number 53285 by maxmathsup by imad last updated on 20/Jan/19 $$let{I}_{\lambda }={\int }_0^{\pi }\frac{xdx}{{cos}^{2}x+{\lambda }^2{sin}^{2}x}with\lambda real$$$$1)findthevalueof{I}_{\lambda }$$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xdx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}}…

Question Number 53271 by Abdo msup. last updated on 19/Jan/19 $$1)calculate{\int }_0^{\mathrm{\infty }}{e}^{-{xt}^2}dtwithx>0$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}^{\mathrm{2}} } \:−{e}^{−\mathrm{2}{t}^{\mathrm{2}} } }{{t}^{\mathrm{2}} }\:{dt}\:\:{by}\:{using} \…