Question

$\int 2^{m x} \cdot 3^{n x} d x$ when $m, n \in N$ is equal to:

• A. $\frac{2^{m x}+3^{n x}}{m \ell n 2+n \ell n 3}+c$
• B. $\frac{(m n) \cdot 2^x \cdot 3^x}{m \ell n 2+n \ell n 3}+c $
• C. $ \frac{2^{m x} \cdot 3^{n x}}{\ln \left(2^m \cdot 3^n\right)}+c$
• D. none of these

Answer 1

Answer: (C)

$I=\int 2^{m x} \cdot 3^{n x} d x=\int\left(2^m \cdot 3^n\right)^x d x=\frac{2^{m x} \cdot 3^{n x}}{\ln \left(2^m \cdot 3^n\right)}+c$