Integrate \(\frac{2x^3 + 2x}{x}\) with respect to x
A
\(\frac{2x^3}{3}\) - 2x + k
B
x3 + 2x + k
C
\(\frac{2x^3}{3}\) + 2x + k
D
x3 - 2x + k
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\int\) \(\frac{2x^3 + 2x}{x}\) = \(\int\) \(\frac{2x^3}{x}\) + \(\frac{2x}{x}\) = \(\int\) (2x2 + 2) dx
\(\frac{2x^2+1}{2 + 1}\) + 2x + k
= \(\frac{2x^3}{3}\)+ 2x + k
Source: Myschool Past Questions Archive (Record #44744)