Evaluate: (i) `intx\ e^x^2\ dx` (ii) `int(e^(2x))/(1+e^x)\ dx`

Explanation

Let's evaluate the given integrals step by step.

### (i) Evaluate the integral \( \int x e^{x^2} \, dx \)

**Step 1: Substitution**
We will use the substitution \( t = e^{x^2} \). Then, we need to find \( dt \):
\[
dt = \frac{d}{dx}(e^{x^2}) \, dx = e^{x^2} \cdot 2x \, dx \implies dx = \frac{dt}{2x e^{x^2}}
...