🔄
u-Substitution Step-by-Step
AP Calculus AB · Unit 6 Integration
Learning Objectives
Identify what to choose as u
Compute du and solve for dx
Rewrite the integral entirely in terms of u
Back-substitute to get answer in terms of x
Strategy
Choose u =
"inner function"
• Look inside compositions
• du should appear (or differ by constant) in the integrand
For definite integrals:
change bounds too!
Tags
u-substitution
integration
chain rule reverse
SELECT INTEGRAL
∫ 2x·cos(x²) dx
∫ x²√(x³+1) dx
∫ eˢⁱⁿˣ·cos x dx
∫ tan(x) dx
∫₀¹ x/(x²+1) dx
∫ x·e^(x²) dx