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
jamb 2022mathematics

The correct answer is B. \(\frac{{2x+1}^4}{8}\) + C

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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