Evaluate the integral ∫0π/2sinxcosx1+sin4x dx\int_0^{\pi/2} \frac{\sin x \cos x}{1 + \sin^4 x} \,dx∫0π/21+sin4xsinxcosxdx.
π8\frac{\pi}{8}8π
π4\frac{\pi}{4}4π
12\frac{1}{2}21
π2\frac{\pi}{2}2π