∫ x d x / √(x⁴ − 1)

What is the result of the integral?

• Option A: 0
• Option B: 1
• Option C: 2
• Option D: Undefined

To solve the integral ∫ x dx / √(x⁴ − 1), we can use a substitution method. Let's set u = x⁴ − 1. Then, the derivative du = 4x³ dx, which means dx = du / (4x³). This substitution helps us rewrite the integral in terms of u.

However, upon analyzing the integral, we notice that the function has a singularity at x = ±1, where the denominator becomes zero. This means the integral is not defined over the entire range of x.

Given these considerations, the correct answer is:

• Option D: Undefined