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Category: Integration

find-the-value-of-f-a-0-x-2-1-x-4-a-4-2-dx-2-calculate-0-x-2-1-x-4-1-2-dx-

Question Number 37602 by prof Abdo imad last updated on 15/Jun/18 $${find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{4}} \:\:\:+{a}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:−\mathrm{1}}{\left({x}^{\mathrm{4}}…

solve-sin-2-x-y-dx-tan-x-dy-0-

Question Number 103089 by  M±th+et+s last updated on 12/Jul/20 $${solve}: \\ $$$$\left({sin}^{\mathrm{2}} \left({x}\right)−{y}\right){dx}−{tan}\left({x}\right){dy}=\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 12/Jul/20 $$\Rightarrow\left\{\mathrm{tanx}\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right\}\centerdot\mathrm{cosx}…