Integrate \(\frac{1 + x}{x^{3}} \mathrm d x\)
A
\(2x^{2} - \frac{1}{x} + k\)
B
\(-\frac{1}{2x^{2}} - \frac{1}{x} + k\)
C
\(-\frac{x^{2}}{2} - \frac{1}{x} + k\)
D
\(x^{2} - \frac{1}{x} + k\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\int \frac{1 + x}{x^{3}} \mathrm d x\)
= \(\int (\frac{1}{x^{3}} + \frac{x}{x^{3}}) \mathrm d x\)
= \(\int (x^{-3} + x^{-2}) \mathrm d x\)
= \(\frac{-1}{2x^{2}} - \frac{1}{x} + k\)
Source: Myschool Past Questions Archive (Record #54926)