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Question Number 82139 by jagoll last updated on 18/Feb/20

∫  ((√(x^4 +x^(−4) +2))/x^3 ) dx

$$\int\:\:\frac{\sqrt{{x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{2}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$

Answered by mind is power last updated on 18/Feb/20

x^4 +x^(−4) +2=(x^2 +x^(−2) )^2

$${x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{2}=\left({x}^{\mathrm{2}} +{x}^{−\mathrm{2}} \right)^{\mathrm{2}} \\ $$

Commented by jagoll last updated on 18/Feb/20

thank you

$${thank}\:{you} \\ $$

Commented by mind is power last updated on 19/Feb/20

withe pleasur to help when i have Time sir

$${withe}\:{pleasur}\:{to}\:{help}\:{when}\:{i}\:{have}\:{Time}\:{sir} \\ $$$$ \\ $$

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