Find $\int \sqrt{ \sec^4 x + \cos^4 x}dx$

Question

Find $\int \sqrt{ \sec^4 x + \cos^4 x} dx$

I tried by taking $\sec^2 x $out of the square root and taking $\cos^2 x $ out of the root, but all my effort goes in vain. So anybody please helps me. Thanks in advance.