Indefinite Integral of Reciprocal of Trigonometric Functions How to evaluate following integral

$$\int \frac{\mathrm dx}{\sin^4x+\cos^4x\:+\sin^2(x) \cos^2(x)}$$

Can you please also give me the steps of solving it?

Divide the numerator & the denominator by $\cos^4x$ to find
$$I=\int\frac{\sec^4x}{\tan^4x+1+\tan^2x}dx$$
Putting $\tan x=y,$
$$I=\int\frac{1+y^2}{1+y^2+y^4}dy=\int\frac{1+\dfrac1{y^2}}{\dfrac1{y^2}+1+y^2}dy$$
$$=\int\frac{1+\dfrac1{y^2}}{\left(y-\dfrac1y\right)^2+3}dy $$
Finally set, $u=y-\dfrac1y=\dfrac{y^2-1}y=-2\cdot\dfrac1{\dfrac{2\tan x}{1-\tan^2x}}=-2\cot2x$
