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.

*

*Divide the numerator by $x^2$ and you have $1+\frac{1}{x^2}$

*Divide the denominator by $x^2$ and you have $x^2+\frac{1}{x^2} =\bigl(x-\frac{1}{x}\bigr)^{2}+2$
