← MATH 01130 · Calculus I
MATH 01130 · Integrals (intro)
u-substitution basics
Definition
Substitution reverses the chain rule. Set u=g(x), du=g′(x)dx, rewrite the integral in u, integrate, then substitute back (or change limits for definite integrals).
Read this
Look for an “inside function” whose derivative (up to constant) is present.
For definite integrals, change limits to u-values and skip returning to x.
If substitution fails, try algebra rewrite or a different technique (parts comes in Calc II).
Drill with flashcards
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Try this
Attempt each problem first, then open the worked solution.
1.Compute ∫(3x+1)⁴ dx and ∫₀¹ 2x e^{x²} dx.