`intsqrt((1+x))dx`

Explanation

To solve the integral \(\int \sqrt{1+x} \, dx\), we will use the substitution method. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = 1 + x \). Then, we differentiate \( t \) with respect to \( x \):
\[ dt = dx \]
This means that \( dx = dt \).
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