Question Number 67342 by mathmax by abdo last updated on 26/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} −{x}\:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 132877 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right).{log}^{\mathrm{2}} \left({x}\right)}{{x}} \\ $$$$\:\:\:\:\:\:\:=\frac{\pi}{\mathrm{24}}\left(\mathrm{12}\gamma^{\:\mathrm{2}} +\pi^{\mathrm{2}} \right)\:….. \\ $$ Answered by…
Question Number 132876 by mnjuly1970 last updated on 17/Feb/21 Commented by Dwaipayan Shikari last updated on 17/Feb/21 $$\phi'\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:\:\phi\left({x}\right){is}\:{defined}\:{in}\:{Q}\mathrm{132877} \\ $$ Terms of Service Privacy Policy…
Question Number 1788 by 112358 last updated on 26/Sep/15 $${Find}\:{the}\:{value}\:{of}\:{Q}\:{if}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{Q}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} {ln}\left(\frac{\mathrm{1}+{sinx}}{\mathrm{1}+{cosx}}\right){dx}\:. \\ $$$$ \\ $$ Commented by John_Haha last updated on 21/Nov/15…
Question Number 132852 by abdullahquwatan last updated on 17/Feb/21 $$\int\left({x}−\mathrm{1}\right)^{{x}+\mathrm{1}} \mathrm{d}{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1778 by 112358 last updated on 23/Sep/15 $${Let}\:{P}\left({t}\right)\:{denote}\:{a}\:{given}\:{cubic} \\ $$$${polynomial}.\:{Find}\:{the}\:{constants} \\ $$$${a}_{\mathrm{1}} ,{u}_{\mathrm{1}} ,{a}_{\mathrm{2}} \:{and}\:{u}_{\mathrm{2}} \:{such}\:{that} \\ $$$$\int_{−\mathrm{1}} ^{\:\mathrm{1}} {P}\left({t}\right){dt}={a}_{\mathrm{1}} {P}\left({u}_{\mathrm{1}} \right)+{a}_{\mathrm{2}} {P}\left({u}_{\mathrm{2}}…
Question Number 1780 by 112358 last updated on 23/Sep/15 $${Find}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi} {f}\left({x}\right){cosxdx} \\ $$$${given}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\mathrm{1}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{coskx}.\: \\ $$ Commented by Rasheed…
Question Number 67310 by mathmax by abdo last updated on 25/Aug/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated…
Question Number 132838 by Ahmed1hamouda last updated on 16/Feb/21 Answered by TheSupreme last updated on 17/Feb/21 $$\int\int\left({x}+{y}\right)^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}−{y}\right){dA} \\ $$$${R}=\left\{\left({x},{y}\right)\mid−\mathrm{1}<{x}−{y}<\mathrm{1},\:\mathrm{1}<{x}+{y}<\mathrm{3}\right\} \\ $$$${set}\:{u}={x}+{y},\:{v}={x}−{y} \\ $$$${R}'=\left\{\left({u},{v}\right)\mid−\mathrm{1}<{v}<\mathrm{1},\mathrm{1}<{u}<\mathrm{3}\right\}…
Question Number 1758 by prakash jain last updated on 18/Sep/15 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{sequence}\:\frac{\mathrm{1}}{{p}},\:{p}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{is}\:\mathrm{divergent}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com