Lesson 12 of 20 · about 16 min

Integration techniques

Differentiating always works by rule; integrating takes some cunning. Two tricks cover most cases you'll meet. Substitution undoes the chain rule, and integration by parts undoes the product rule. You'll see substitution as stretching an axis, check an answer the reliable way (by differentiating it), and use both to answer a question about the pool, then learn when to stop and let the computer do it numerically.