Indefinite Integrals
11. Integral of type $\int {\frac{{{x^2} \pm 1}}{{{x^4} + k{x^2} + 1}}dx} $
11. Integral of type $\int {\frac{{{x^2} \pm 1}}{{{x^4} + k{x^2} + 1}}dx} $
In this type of integral $k$ is any constant. To solve this, divide numerator and denominator by ${{x^2}}$ and put $$x \mp \frac{1}{x} = t \Rightarrow \left( {1 \mp \frac{1}{{{x^2}}}} \right)dx = dt$$
