Integrate $ (2x+1)^3 $

Assessment: JAMB UTME - Mathematics - 2022 Subject: General Mathematics

Question 1 Report

\frac{{2 x + 1}^{3}}{8}

+ C

\frac{{2 x + 1}^{4}}{8}

+ C

\frac{{2 x + 1}^{4}}{4}

+ C

\frac{{2 x + 1}^{2}}{6}

+ C

Answer Details

Recall chain rule:

u = 2x +1; du = 2dx → dx = $\frac{d u}{2}$
u $^{3}$ = ∫ u $^{3}$ $\frac{d u}{2}$ → $\frac{1}{2}$ ∫ u $^{3}$

= $\frac{1 * u^{4}}{2 * 4}$

= $\frac{u^{4}}{8}$ → $\frac{{2 x + 1}^{4}}{8}$ + C

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