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Question-175553




Question Number 175553 by BHOOPENDRA last updated on 02/Sep/22
Answered by Frix last updated on 03/Sep/22
∫_0 ^1 (((x^n −1)(x−1))/(x^(n+3) −1))dx=^((let t=(1/x))) ∫_∞ ^1 (((t^n −1)(t−1))/(t^(n+3) −1))dt  ⇒  answer is 0
$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\left({x}^{{n}} −\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{{x}^{{n}+\mathrm{3}} −\mathrm{1}}{dx}\overset{\left(\mathrm{let}\:{t}=\frac{\mathrm{1}}{{x}}\right)} {=}\underset{\infty} {\overset{\mathrm{1}} {\int}}\frac{\left({t}^{{n}} −\mathrm{1}\right)\left({t}−\mathrm{1}\right)}{{t}^{{n}+\mathrm{3}} −\mathrm{1}}{dt} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:\mathrm{0} \\ $$

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