Question Number 67539 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{du}}{\mid{u}+{z}\mid^{\mathrm{2}} }\:\:{if}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{and}\:−\pi<\theta<\pi \\ $$ Commented by ~ À ® @ 237…
Question Number 1997 by prakash jain last updated on 29/Oct/15 $${A}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…. \\ $$$${B}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…. \\ $$$${A}−{B}=? \\ $$ Commented by Rasheed Soomro last updated on 30/Oct/15…
Question Number 67530 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{n}−\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}{n}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$ Commented by ~ À ® @ 237…
Question Number 67528 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{1}+{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$ Commented by ~ À ® @ 237…
Question Number 67531 by mathmax by abdo last updated on 28/Aug/19 $${prove}\:{that}\:{cos}\left(\pi{z}\right)\:=\prod_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}−\frac{{z}^{\mathrm{2}} }{\left(\frac{\mathrm{1}}{\mathrm{2}}+{n}\right)^{\mathrm{2}} }\right) \\ $$ Commented by ~ À ® @ 237…
Question Number 67527 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$$$ \\ $$ Commented by ~ À ®…
Question Number 67526 by mathmax by abdo last updated on 28/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{3}+\mathrm{2}{sinx}\:+{cosx}} \\ $$ Commented by mathmax by abdo last updated on 31/Aug/19…
Question Number 67525 by mathmax by abdo last updated on 28/Aug/19 $${let}\:{a}>{b}>\mathrm{0}\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{\left({a}+{bsinx}\right)^{\mathrm{2}} } \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 67517 by mathmax by abdo last updated on 28/Aug/19 $${let}\:{z}\:\in{C}\:{and}\:\mid{z}\mid<\mathrm{1}\:\:{prove}\:{that} \\ $$$$\frac{{z}}{\mathrm{1}−{z}^{\mathrm{2}} }\:+\frac{{z}^{\mathrm{2}} }{\mathrm{1}−{z}^{\mathrm{4}} }\:+…..+\frac{{z}^{\mathrm{2}^{{n}} } }{\mathrm{1}−{z}^{\mathrm{2}^{{n}+\mathrm{1}} } }+…=\frac{{z}}{\mathrm{1}−{z}} \\ $$$$\frac{{z}}{\mathrm{1}+{z}}\:+\frac{\mathrm{2}{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{2}} }\:+….+\frac{\mathrm{2}^{{n}}…
Question Number 133051 by mnjuly1970 last updated on 18/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:{evaluate}:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{\mathrm{2}} \:\mathrm{2}^{{n}+\mathrm{1}} }=?? \\ $$ Terms of Service Privacy Policy Contact:…