Question

$\int 9^{18x+4}dx$ is equal to
(where $C$ is the constant of integration)

• A. $\frac{9^{18x+4}}{36\ln 3}+C$
• B. $\frac{9^{18x+4}}{18\ln 9}+C$
• C. $\frac{9^{18x+4}}{9\ln 18}+C$
• D. $\frac{9^{18x+4}}{18\ln 18}+C$

Answer 1

Answer: (A), (B)

$\frac{9^{18x+4}}{18\ln 9}+C$

$\int 9^{18x+4}dx=\frac{9^{18x+4}}{\ln 9}\times \frac{1}{18}+C$
$(\because \int a^{bx+c}dx=\frac{a^{bx+c}}{\ln a}\times \frac{1}{b}+C,a>0,b\ne 0)$
$\Rightarrow \frac{9^{18x+4}}{\ln 3^2}\times \frac{1}{18}+C=\frac{9^{18x+4}}{36\ln 3}+C$