令x² = tanθ,2x dx = sec²θ dθ∫ x/(1 + x^4) dx= ∫ x/(1 + tan²θ) • sec²θ dθ/(2x)= (1/2)∫ sec²θ/sec²θ dθ= (1/2)θ + C= (1/2)arctan(x²) + C