Integrate the function `(x e^x)/((1+x)^2)`

Explanation

To solve the integral \(\int \frac{x e^x}{(1+x)^2} \, dx\), we can follow these steps:

### Step 1: Rewrite the integrand
We start by rewriting the integrand \(\frac{x e^x}{(1+x)^2}\) in a more manageable form. We can express \(x\) as \( (1+x) - 1 \):
\[ \frac{x e^x}{(1+x)^2} = \frac{(1+x - 1)e^x}{(1+x)^2} = \frac{(1+x)e^x - e^x}{(1+x)^2} = \frac{e^x}{1+x} - \frac{e^x}{(1+x)^2} \]

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