Integrate (2x+1)\(^3\)
MATHEMATICS
JAMB 2022
Integrate (2x+1)\(^3\)
- A. \(\frac{{2x+1}^3}{8}\) + C
- B. \(\frac{{2x+1}^4}{8}\) + C
- C. \(\frac{{2x+1}^4}{4}\) + C
- D. \(\frac{{2x+1}^2}{6}\) + C
Correct Answer: B. \(\frac{{2x+1}^4}{8}\) + C
Explanation
Recall chain rule:
u = 2x +1; du = 2dx → dx = \(\frac{du}{2}\)
u\(^3\) =∫u\(^3\) \(\frac{du}{2}\) → \(\frac{1}{2}\)∫u\(^3\)
= \(\frac{1*u^4}{2*4}\)
= \(\frac{u^4}{8}\) → \(\frac{{2x+1}^4}{8}\) + C
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