Question Number 28999 by abdo imad last updated on 03/Feb/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} }{\:\sqrt{{t}}}{dt}=\:{e}^{{i}\frac{\pi}{\mathrm{4}}} \:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{ix}} }{\:\sqrt{{x}}}{dx}. \\ $$ Commented by abdo imad last…
Question Number 28996 by abdo imad last updated on 03/Feb/18 $${find}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\:\frac{{x}^{\mathrm{2}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)}{dx}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 28995 by abdo imad last updated on 02/Feb/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{2}{t}\right)}{\mathrm{3}−{cost}}\:{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94530 by i jagooll last updated on 19/May/20 Commented by PRITHWISH SEN 2 last updated on 19/May/20 $$\int\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\mathrm{x}^{\mathrm{3}} .\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}}\:\:\:\:\mathrm{put}\:\mathrm{x}^{\mathrm{3}} +\mathrm{1}\:=\:\mathrm{t}^{\mathrm{3}} \:\Rightarrow\mathrm{x}^{\mathrm{2}}…
Question Number 28994 by abdo imad last updated on 02/Feb/18 $${find}\:\:{A}_{{n}} =\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28992 by abdo imad last updated on 02/Feb/18 $${L}\:{means}\:{laplace}\:{transform}\:{find}\:\:{L}\left({e}^{{at}} \right)\left({s}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28993 by abdo imad last updated on 02/Feb/18 $${L}\:{means}\:{laplacr}\:{trsnsform}\:{find}\:{L}\:\left({sin}\left({at}\right)\right) \\ $$$${and}\:{L}\left({cos}\left({at}\right)\right). \\ $$ Answered by sma3l2996 last updated on 03/Feb/18 $${L}\left({sin}\left({at}\right)\right)=\int_{\mathrm{0}} ^{\infty} {sin}\left({at}\right){e}^{−{st}}…
Question Number 28990 by abdo imad last updated on 02/Feb/18 $${calculate}\:\int_{\gamma} \:\:\:\frac{{e}^{{z}} }{\left({z}−\mathrm{1}\right)\left({z}+\mathrm{3}\right)^{\mathrm{2}} }{dz}\:{with}\:\gamma\:{id}\:{the}\:{positif} \\ $$$${circle}\:\gamma=\left\{{z}\in{C}/\:\mid{z}\mid=\frac{\mathrm{3}}{\mathrm{2}}\right\}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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 28989 by abdo imad last updated on 02/Feb/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} }{dx}. \\ $$ Commented by abdo imad last updated on 04/Feb/18…