Evaluate: ∫1/(cos4x+sin4x)dx

Let I = ∫dx/(cos4x+sin4x) = ∫1/(cos4x(1+tan4x))dx = ∫(sec2x.sec2x)dx/(1+tan4x) = ∫(1+tan2x)sec2xdx/(1+tan4x)
Put tanx = t ⇒ sec2xdx = dt
= ∫(1+t2)dt/(1+t4) = ∫(1/t2 + 1)dt/(t2 + 1/t2)
= ∫(1 + 1/t2)dt/((t - 1/t)2 + 2)
Put t - 1/t = z ⇒ (1 + 1/t2)dt = dz
= ∫dz/(z2 + 2) = 1/√2tan⁻¹(z/√2) + C
= 1/√2tan⁻¹((t - 1/t)/√2) + C
= 1/√2tan⁻¹((tanx - cotx)/√2) + C