Question

$\int (4x+5{)}^{6}dx$ is equal to
(where $C$ is the constant of integration)

• A. $\frac{(4x+5{)}^7}{14}+C$
• B. $\frac{(4x+5{)}^7}{7}+C$
• C. $\frac{(4x+5{)}^7}{56}+C$
• D. $\frac{(4x+5{)}^7}{28}+C$

Answer 1

The correct option is D $\frac{(4x+5{)}^7}{28}+C$

$\int (4x+5{)}^6=\frac{(4x+5{)}^{6+1}}{6+1}\times \frac{1}{4}+C$
$(\because \underset{}{\overset{}{\int }}(ax+b{)}^{n}dx=\frac{(ax+b{)}^{n+1}}{n+1}\times \frac{1}{a},n\ne \{-1,0\},a\ne 0)$
$\Rightarrow \underset{}{\overset{}{\int }}(4x+5{)}^{6}dx=\frac{(4x+5{)}^7}{28}+C$