Question Number 31057 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} }\:{dx}.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31054 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31055 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}+\mathrm{4}\right)}\:. \\ $$ Commented by abdo imad last updated on 03/Mar/18…
Question Number 31056 by abdo imad last updated on 02/Mar/18 $${find}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:−\mathrm{2}{xcos}\alpha\:+\mathrm{1}}\:\:{with}\:\mathrm{0}<\alpha<\pi\:. \\ $$ Commented by abdo imad last updated on 03/Mar/18 $${I}=\:\int_{\mathrm{1}}…
Question Number 31052 by abdo imad last updated on 02/Mar/18 $${let}\:{give}\:\mathrm{0}<{a}<{b}\:\:{find}\:\int_{{a}} ^{{b}} \:\:\frac{{lnx}}{{x}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31053 by abdo imad last updated on 02/Mar/18 $${let}\:\lambda\:\in{R}\:{and}\:{a}>\mathrm{0}\:\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{ax}} {cos}\left(\lambda{x}\right){dx}\:. \\ $$ Commented by abdo imad last updated on 03/Mar/18 $${let}\:{put}\:{I}=\int_{\mathrm{0}}…
Question Number 31051 by abdo imad last updated on 02/Mar/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}} \:−{e}^{−{bx}} }{\mathrm{1}−\:{e}^{−{x}} }\:{dx}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31049 by abdo imad last updated on 02/Mar/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{−{x}} {dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 162117 by CM last updated on 27/Dec/21 Commented by cortano last updated on 27/Dec/21 $$\:\int\:{x}^{\mathrm{2}} \:\sqrt{\mathrm{4}\:−\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$$$\:\left[\:\mathrm{1}−{x}\:=\:\mathrm{2sin}\:{t}\:\Rightarrow{dx}=−\mathrm{2cos}\:{t}\:{dt}\:\right] \\ $$$$\:\int\:\left(\mathrm{1}−\mathrm{2sin}\:{t}\right)^{\mathrm{2}} \:\left(−\mathrm{2cos}\:^{\mathrm{2}} {t}\right){dt}…
Question Number 31048 by abdo imad last updated on 02/Mar/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{\frac{\pi}{\mathrm{2}}\:−{arctanx}}{{x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com