Three complex and real integrals

Compute:

1. \(\displaystyle\int_\gamma e^{2z^2}\,dz\), where \(\gamma\) is the counterclockwise square of side length \(2\) centered at \(0\);

2. \(\displaystyle\int_{|z|=5}\left(\frac1z-\frac1{z^2}\right)^3\,dz\);

3. \(\displaystyle\int_{-\infty}^{\infty}\frac{x+1}{(x^2+1)^2}\,dx\).