The value of $\int\frac{dx}{x^4+5x^2+4}$ is:
Answer & explanation
Correct answer: option 4
$I=\int\frac{dx}{x^4+5x^2+4}=\int\frac{dx}{(x^2+1)(x^2+4)}=\int\frac{1}{3}[\frac{1}{x^2+1}-\frac{1}{x^2+4}]dx⇒I=\frac{1}{3}\tan^{-1}x-\frac{1}{6}\tan^{-1}(\frac{x}{2})+C$