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Question Number 25183 by ajfour last updated on 06/Dec/17

Prove that  ∫_0 ^(  ∞) ((x^6 dx)/((a^4 +x^4 )^2 ))= ((3π(√2))/(16a))   ,  (a>0) .

$${Prove}\:{that} \\ $$ $$\int_{\mathrm{0}} ^{\:\:\infty} \frac{{x}^{\mathrm{6}} {dx}}{\left({a}^{\mathrm{4}} +{x}^{\mathrm{4}} \right)^{\mathrm{2}} }=\:\frac{\mathrm{3}\pi\sqrt{\mathrm{2}}}{\mathrm{16}{a}}\:\:\:,\:\:\left({a}>\mathrm{0}\right)\:. \\ $$

Commented byprakash jain last updated on 05/Dec/17

should the answer be ((3π(√2))/(16a))

$$\mathrm{should}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{be}\:\frac{\mathrm{3}\pi\sqrt{\mathrm{2}}}{\mathrm{16}{a}} \\ $$

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