Category: Integration

Question Number 28988 by abdo imad last updated on 02/Feb/18 $${let}\:{give}\:\mathrm{0}<\alpha<\mathrm{1}\:{find}\:{in}\:{terms}\:{of}\:\alpha\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{x}^{\alpha} \left(\mathrm{1}+{x}\right)}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 94520 by john santu last updated on 19/May/20 $$\int\:\sqrt{{e}^{\mathrm{4}{x}} +\mathrm{1}}\:{dx}\: \\ $$ Answered by niroj last updated on 19/May/20 $$\:\:\int\sqrt{\left(\mathrm{e}^{\mathrm{x}} \right)^{\mathrm{4}} +\mathrm{1}}\:\:\mathrm{dx}\:\: \\…

Question Number 28985 by abdo imad last updated on 02/Feb/18 $${let}\:{give}\:{I}_{{m},{a}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{1}\right){verify}\:{that}\:{I}_{{m},\mathrm{1}} ={lim}_{{a}\rightarrow\mathrm{1}} \:{I}_{{m},{a}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{sin}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}}…

Question Number 28984 by abdo imad last updated on 02/Feb/18 $${find}\:{F}\left(\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\right)\:{F}\:{means}\:{fourier}\:{transform}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 94510 by i jagooll last updated on 19/May/20 $$\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}\:{x}.\mathrm{cos}\:{x}}{dx}\: \\ $$ Commented by PRITHWISH SEN 2 last updated on 19/May/20 $$\int\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}.\sqrt{\mathrm{tanx}}}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:\:\mathrm{now}\:\mathrm{put}\:\mathrm{tanx}=\mathrm{t}^{\mathrm{2}} \\…