Definite Integral $\int{x^2+1 \over x^4+1}$ Evaluate
$$\int_0^{\infty}{x^2+1 \over x^4+1}$$
I tried using Integration by parts , 
$$\frac{{x^3 \over 3 }+x}{x^4+1}+\int\frac{{x^3 \over 3 }+x}{(x^4+1)^2}.4x^3.dx$$
First term is zero
But  it got me no where.
Any hints.

Hint: $$\frac{x^2+1}{x^4+1}=\frac1{2\left(x^2+\sqrt2x+1\right)}+\frac1{2   \left(x^2-\sqrt2x+1\right)}.$$
