Integrate \(\frac{1 + x}{x^{3}} \mathrm d x\)
- \(2x^{2} - \frac{1}{x} + k\)
-
\(-\frac{1}{2x^{2}} - \frac{1}{x} + k\)
- \(-\frac{x^{2}}{2} - \frac{1}{x} + k\)
- \(x^{2} - \frac{1}{x} + k\)
The correct answer is: B
Explanation
\(\int \frac{1 + x}{x^{3}} \mathrm d x\)
= \(\int (\frac{1}{x^{3}} + \frac{x}{x^{3}}) \mathrm d x\)
= \(\int (x^{-3} + x^{-2}) \mathrm d x\)
= \(\frac{-1}{2x^{2}} - \frac{1}{x} + k\)
There is an explanation video available .