If dxx ( x^4-1 )= 1k sec^-1 ⁡ (x^k ), then the value of k is equal to

Question

Accepted Answer

Correct answer: B. (b) Given dxx x^4-1= 1k sec^-1 ⁡ (x^k ) 12 2 xdxx^2 x^4-1= 1k sec^-1 ⁡ (x^k ) Let x^2=t ⇒2 xdx= dt = 12 dtt t^2-1= 12 sec^-1 ⁡t ⇒ 1k sec^-1 ⁡ (x^k )= 12 sec^-1 ⁡ (x^2 ) ⇒k=2

$If \int \frac{dx}{x ( x ^{4} - 1 )} = \frac{1}{k} sec^{- 1} (x^{k}), then the value of k is equal to$

Solution

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