Find (int frac{x^{3} + 5x + 1}{x^{3}} mathrm {d} x)
-
A.
(x^{2} + 10x + c) -
B.
(x + frac{5}{3}x^{3} + x^{4} + c) -
C.
(x – 5x^{2} – 2x^{3} + c) -
D.
(x – frac{5}{x} – frac{1}{2x^{2}} + c)
Correct Answer: Option D
Explanation
(frac{x^{3} + 5x + 1}{x^{3}} equiv 1 + frac{5}{x^{2}} + frac{1}{x^{3}})
(equiv int (1 + frac{5}{x^{2}} + frac{1}{x^{3}}) mathrm {d} x = int (1 + 5x^{-2} + x^{-3}) mathrm {d} x)
= ((x – 5x^{-1} – frac{1}{2}x^{-2} + c))
= (x – frac{5}{x} – frac{1}{2x^{2}} + c).