Question

$\int a^{8x+9}dx,a>0$ is equal to
(where $C$ is constant of integration)

• A. $\frac{a^{8x+9}}{8\ln a}+C$
• B. $\frac{a^{8x+9}}{9\ln a}+C$
• C. $\frac{a^{8x+9}}{a\ln 9}+C$
• D. $\frac{a^{8x+9}}{a\ln 8}+C$

Answer 1

The correct option is A $\frac{a^{8x+9}}{8\ln a}+C$

$\int a^{8x+9}dx=\frac{a^{8x+9}}{\ln a}\times \frac{1}{8}+C$
$(\because \int a^{bx+c}dx=\frac{a^{bx+c}}{\ln a}\times \frac{1}{b}+C,a>0,b\ne 0)$