Category: Integration

Question Number 28823 by abdo imad last updated on 30/Jan/18 $${find}\:\:{I}\:=\:\int_{−\infty} ^{+\infty} \:\:\frac{\left({x}−\mathrm{1}\right){cosx}}{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}}{dx}\:{and} \\ $$$${J}=\:\int_{−\infty} ^{+\infty} \:\:\frac{\left({x}−\mathrm{1}\right){sinx}}{{x}^{\mathrm{2}} −\mathrm{2}{x}\:+\mathrm{2}}\:{dx}. \\ $$ Terms of Service Privacy…

Question Number 94354 by  M±th+et+s last updated on 18/May/20 $${by}\:{using}\:{ostrogadski}\:{method}\:{solve}\:{this} \\ $$$${integral} \\ $$$$\int\frac{\mathrm{3}{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{12}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by MJS…

Question Number 28819 by abdo imad last updated on 30/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${by}\:{using}\:{derivation}\:{under}\:\int\:\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy Policy…

Question Number 28815 by abdo imad last updated on 30/Jan/18 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{2}{cos}^{\mathrm{2}} {x}\:+{sin}^{\mathrm{2}} {x}}\:. \\ $$ Answered by mrW2 last updated on 31/Jan/18 $$\int_{\mathrm{0}}…

Question Number 28813 by abdo imad last updated on 30/Jan/18 $${let}\:{give}\:{F}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } {dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$${find}\:\:\frac{{dF}}{{dt}}\left({t}\right). \\ $$$$ \\ $$ Terms of…