Question Number 165853 by mathlove last updated on 09/Feb/22 Answered by MJS_new last updated on 09/Feb/22 $$\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}+\mathrm{2}\right)^{\mathrm{4}} \left({x}−\mathrm{1}\right)^{\mathrm{4}} }{dx}= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\right] \\ $$$$=\frac{\mathrm{40}{x}^{\mathrm{5}} +\mathrm{100}{x}^{\mathrm{4}} −\mathrm{140}{x}^{\mathrm{3}}…
Question Number 34771 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{A}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right){dx} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right)\:\:\:\:\left({x}\in{R}\right) \\ $$ Commented by abdo mathsup 649…
Question Number 34720 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{B}\left({p},{q}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{p}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{q}−\mathrm{1}} {dx} \\ $$$${calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{2}}\:,\frac{\mathrm{2}}{\mathrm{3}}\right)\:. \\ $$ Terms of…
Question Number 34715 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant{y}\leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({y}^{\mathrm{2}} \:+\mathrm{3}\right)}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34716 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{{w}} {x}\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:\:{dxdy} \\ $$$${w}\:=\left\{\left({x},{y}\right)/\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{3}\:\right\}\: \\ $$ Commented by prof…
Question Number 34717 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{I}_{{n}} =\:\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\right]^{\mathrm{2}} } \:\:\:\:\:\frac{\sqrt{{xy}}\:{dxdy}}{\mathrm{2}\:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$$${find}\:{lim}\:{I}_{{n}} \:{when}\:{n}\rightarrow+\infty. \\ $$ Commented by…
Question Number 165787 by daus last updated on 08/Feb/22 $${find}\:\:\int{cos}^{\mathrm{3}} {x}\:{dx}\:? \\ $$ Answered by aleks041103 last updated on 08/Feb/22 $${cos}^{\mathrm{3}} {x}\:=\:{cosx}\left(\mathrm{1}−{sin}^{\mathrm{2}} {x}\right)= \\ $$$$={cosx}−{cosxsin}^{\mathrm{2}}…
Question Number 34714 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}} \left({x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} \right){dxdy} \\ $$ Commented by math khazana by…
Question Number 34713 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{a}>\mathrm{0}\:\:{calculate}\:\int\int_{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{3}} \:\frac{\mathrm{1}}{\mathrm{2}\:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}. \\ $$ Commented by math khazana by…
Question Number 165757 by Zaynal last updated on 07/Feb/22 Answered by Mathspace last updated on 08/Feb/22 $${p}\left({x}\right)=\prod_{{n}=\mathrm{1}} ^{\mathrm{100}} \left({x}+{n}\right)\:\Rightarrow\frac{{p}^{'} \left({x}\right)}{{p}\left({x}\right)} \\ $$$$=\sum_{{n}=\mathrm{1}} ^{\mathrm{100}} \frac{\mathrm{1}}{{x}+{n}}\:\Rightarrow \\…