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