`int b^(x+a) " dx "`

Answer

To solve the integral \( \int b^{(x+a)} \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int b^{(x+a)} \, dx \]
We can rewrite \( b^{(x+a)} \) as:
\[ b^{(x+a)} = b^x \cdot b^a \]
Thus, we have:
\[ I = \int b^x \cdot b^a \, dx \]

### Step 2: Factor Out the Constant
Since \( b^a \) is a constant with respect to \( x \), we can factor it out of the integral:
\[ I = b^a \int b^x \, dx \]

### Step 3: Use the Integration Formula
We know the formula for the integral of \( b^x \):
\[ \int b^x \, dx = \frac{b^x}{\log b} + C \]
Using this formula, we can substitute back into our integral:
\[ I = b^a \left( \frac{b^x}{\log b} + C \right) \]

### Step 4: Distribute the Constant
Now, we distribute \( b^a \):
\[ I = \frac{b^a b^x}{\log b} + b^a C \]
We can combine the constants:
\[ I = \frac{b^{(x+a)}}{\log b} + C_1 \]
where \( C_1 = b^a C \).

### Final Result
Thus, the final result for the integral is:
\[ \int b^{(x+a)} \, dx = \frac{b^{(x+a)}}{\log b} + C_1 \]