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
Explanation
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
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