If ∫ d x x x 4 - 1 = 1 k sec - 1 x k , then the value of k =

Step-by-step solution

Given that ∫ d x x x 4 - 1 Put x 2   =   sec θ ⇒ 2 x   d x   =   sec θ   tan θ   d θ   =   ∫ sec θ   tan θ d θ 2 sec θ   tan θ   =   ∫ 1 2 d θ = θ 2 = 1 2 sec - 1 x 2   +   c Given that it's equal to 1 k sec - 1 x k By comparing k   = 2 .