Question

Integrate the following functions with respect to x: $\int {(6x+2)}^{3}dx$

• A. $\frac{{(6x+2)}^3}{6}+c_1$
• B. $\frac{{(6x+2)}^4}{12}+c_1$
• C. $\frac{{(6x+2)}^3}{12}+c_1$
• D. $\frac{{(6x+2)}^4}{24}+c_1$

Answer 1

The correct option is D $\frac{{(6x+2)}^4}{24}+c_1$

$\int {(6x+2)}^{3}dx=\frac{1}{6}\int X^{3}dX$ where $X=6x+2$
$=\frac{1}{6}\left(\frac{X^4}{4}\right)+c_1=\frac{{(6x+2)}^4}{24}+c_1$