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.

\(-12x^{-4} - 14x + 5\)

Correct answer is A

\(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\)

= \(\frac{4x^{-3 + 1}}{-3 + 1} - \frac{7x^{2 + 1}}{2 + 1} + \frac{5x^{1 + 1}}{1 + 1} - 6x\)

= \(-2x^{-2} - \frac{7}{3} x^3 + \frac{5}{2} x^2 - 6x\)