Obtain the following integrals :
`int(6^(4)+9^(6))dx`.

Options

A. `(6^(4)+9^(6))x`
B. `(6^(4)+9^(6))`
C. `0`
D. `(6^(5)+9^(7))x`

Explanation

To solve the integral \( \int (6^4 + 9^6) \, dx \), we will follow these steps:

### Step 1: Simplify the expression inside the integral
First, we need to evaluate the constants \( 6^4 \) and \( 9^6 \).

Calculating \( 6^4 \):
\[ 6^4 = 6 \times 6 \times 6 \times 6 = 1296 \]

Calculating \( 9^6 \):
\[ 9^6 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 531441 \]

Now, we can rewrite the integral:
\[ \int (6^4 + 9^6) \, dx = \int (1296 + 531441) \, dx \]

### Step 2: Combine the constants
Now, add the two constants together:
\[ 1296 + 531441 = 532737 \]

So, the integral now becomes:
\[ \int 532737 \, dx \]

### Step 3: Integrate the constant
The integral of a constant \( c \) with respect to \( x \) is given by:
\[ \int c \, dx = cx + C \]
where \( C \) is the constant of integration.

Thus, we have:
\[ \int 532737 \, dx = 532737x + C \]

### Final Answer
The final result of the integral is:
\[ \int (6^4 + 9^6) \, dx = 532737x + C \]

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