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A.
\(2x^{2} - \frac{1}{x} + k\)
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B.
\(-\frac{1}{2x^{2}} - \frac{1}{x} + k\)
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C.
\(-\frac{x^{2}}{2} - \frac{1}{x} + k\)
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D.
\(x^{2} - \frac{1}{x} + k\)
Correct Answer: Option B
Explanation
\(\int \frac{1 + x}{x^{3}} \mathrm d x\)
= \(\int (\frac{1}{x^{3}} + \frac{x}{x^{3}}) \mathrm d x\)
= \(\int (x^{-3} + x^{-2}) \mathrm d x\)
= \(\frac{-1}{2x^{2}} - \frac{1}{x} + k\)
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