Integral ∫\( (5x^3 + 7x^2 − 2x + 5)\)dx
A
\( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)
B
\( \frac{5x^4}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)
C
\( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)
D
\( \frac{2x^2}{3} + \frac{x}{5} - C \)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\int (5x^{3} + 7x^{2} - 2x + 5) \mathrm d x\)
= \(\frac{5x^{4}}{4} + \frac{7x^{3}}{3} - \frac{2x^{2}}{2} + 5x + c\)
= \(\frac{5x^{4}}{4} + \frac{7x^{3}}{3} - x^{2} + 5x + c\)
Source: Myschool Past Questions Archive (Record #40744)