The integral $\int \frac{d x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ equals ________.

$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+C$ $\left(x^4+1\right)^{\frac{1}{4}}+C$ $-\left(x^4+1\right)^{\frac{1}{4}}+C$ $-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+C$

$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+C$

The correct answer is Option (4) - $-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+C$