Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\).
A
\(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)
B
\(2x^2 + \frac{7}{3} x^3 - 5x + 6\)
C
\(12x^2 + 14x - 5\)
D
\(-12x^{-4} - 14x + 5\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\)
= \(\frac{4x^{-3 + 1}}{-3 + 1} - \frac{7x^{2 + 1}}{2 + 1} + \frac{5x^{1 + 1}}{1 + 1} - 6x\)
= \(-2x^{-2} - \frac{7}{3} x^3 + \frac{5}{2} x^2 - 6x\)
Source: Myschool Past Questions Archive (Record #55379)