Integrate (2x+1)\(^3\)
- \(\frac{{2x+1}^3}{8}\) + C
-
\(\frac{{2x+1}^4}{8}\) + C
- \(\frac{{2x+1}^4}{4}\) + C
- \(\frac{{2x+1}^2}{6}\) + C
The correct answer is: B
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
There is an explanation video available .