Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

Assessment: WAEC SSCE - Further Mathematics - 2015 (Objective) Subject: Further Mathematics

Question 1 Report

Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

Answer Details
We can write the given expression as: $$\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x = \int \left(1 + \frac{5}{x^{2}} + \frac{1}{x^{3}}\right) \mathrm {d} x$$ Now, we integrate each term separately: $$\int \mathrm {d} x + 5 \int \frac{1}{x^{2}} \mathrm {d} x + \int \frac{1}{x^{3}} \mathrm {d} x = x - \frac{5}{x} - \frac{1}{2x^{2}} + c$$ Therefore, the correct option is: $$\boxed{x - \frac{5}{x} - \frac{1}{2x^{2}} + c}$$
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