Calculus › Section E · Integrals › Topic E.5
Integration by substitution
Many integrals hide a reversed chain rule inside them. Renaming the inner function as u untangles them, and this one technique multiplies your integration power several-fold.
In this topic
- Integrals with layers
- The pattern to hunt
- The five-step routine
- Worked example: the power pattern
- Adjusting a constant mismatch
- Worked example: a constant to repair
- The linear-inside shortcut
- Worked example: definite integral, limits changed
- Symmetry shortcuts
- Knowing when substitution cannot work
- Common mistakes to avoid
- Key takeaways
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Standards: 6