Integration rules extend basic integrals. (1) Substitution (u-substitution): Let u = g(x), du = g'(x)dx. Then ∫f(g(x))g'(x)dx = ∫f(u)du. Example: ∫2x(x²+1)³ dx. Let u = x²+1, du = 2x dx. Then ∫u³ du = u⁴/4 = (x²+1)⁴/4 + C. (2) Integration by parts: ∫u dv = uv - ∫v du. Choose u using LIATE (Logarithmic, Inverse, Algebraic, Trigonometric, Exponential). Exam tip: Recognize when each rule applies. Substitution for composite functions. By parts for products. Practice: Complex integrals requiring rule selection.