Calculus 11 min read

Integration Rules Cheat Sheet: Formulas & U-Substitution Guide

A comprehensive reference guide for calculus integrals. Master indefinite and definite integration rules, integration by parts, and substitution techniques.

Table of Contents

Mastering Integral Calculus

Integration is the reverse operation of differentiation (antiderivative). It is used to calculate net accumulation, totals, and areas under curves.

Essential Integration Formulas

  • Power Rule: ∫ xⁿ dx = (xⁿ⁺¹ / (n + 1)) + C
  • Exponential Rule: ∫ eᵏˣ dx = (1/k) · eᵏˣ + C
  • Trig Integrals: ∫ sin(x) dx = −cos(x) + C | ∫ cos(x) dx = sin(x) + C
  • Integration by Parts: ∫ u dv = u·v − ∫ v du
  • U-Substitution: Set u = g(x), du = g'(x)dx to simplify complex composite integrals.
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Updated: August 11, 2026

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