Find the ∫ 12x^-5 √- 3x^-4 × 1 dx?

2/3(- 3x^-4 + 1)^(3/2) + c

4(- 3x^-4 + 1)^(3/2) + c

8(- 3x^-4 + 1)^(3/2) + c

None of these

Given ∫12x⁻⁵ √(-3x⁻⁴ + 1) dx

Let u = -3x⁻⁴ + 1

du/dx = 12x⁻⁵

du = 12x⁻⁵ dx

∫√u du = ∫u^(1/2) du

= (2/3)u^(3/2) + C

Substituting back u = -3x⁻⁴ + 1:

= (2/3)(-3x⁻⁴ + 1)^(3/2) + C