The value of `int2^("mx").3^("nx")dx` (when m, `n in N`) is equal to:

Options

A. `(2^(mx)+3^(nx))/(m" ln "2+n" ln "3)+c`
B. `(e^(m" ln "2+n" ln "3)+C)/(m" ln "2+n" ln "3)`
C. `(2^("mx").3^("nx"))/(" ln "(2^(m).3^(n))+C`
D. `((mn).2^(x).3^(x))/(m" ln "2+n" ln "3)+C`

Explanation

To solve the integral \( \int 2^{mx} \cdot 3^{nx} \, dx \), where \( m, n \in \mathbb{N} \), we can follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int 2^{mx} \cdot 3^{nx} \, dx \]

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