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Integrate (2x+1) $^3$ ...

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

View answer & explanation

Correct answer is B

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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