Question

$\int (2-3x{)}^{3}dx$ is equal to
(where $C$ is the constant of integration)

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

Answer 1

The correct option is C

$\frac{-(2-3x{)}^4}{12}+C$

$\int (2-3x{)}^{3}dx=\frac{(2-3x{)}^{3+1}}{3+1}\times \frac{1}{-3}+C$
$(\because \int (ax+b{)}^{n}dx=\frac{(ax+b{)}^{n+1}}{n+1}\times \frac{1}{a},n\ne \{-1,0\},a\ne 0)$
$\Rightarrow \int (2-3x{)}^{3}dx=\frac{-(2-3x{)}^4}{12}+C$