U-Substitution Guide
Integrate by substitution step by step: spot the inner function, change variables, integrate, substitute back.
U-substitution reverses the chain rule: look for an inner function g(x) whose derivative g′(x) also appears in the integrand.
① Answer
② Steps
③ Why it works
U-substitution is the chain rule in reverse. If the integrand contains a composite function f(g(x)) and (a constant multiple of) g′(x), setting u = g(x) collapses the whole integral into ∫f(u)du — usually a plain power rule. The final step is non-negotiable: substitute back to x, because the answer must live in the original variable.