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Integration by Substitution: In Stages

- Evaluate a derivative by the chain rule. Ask students what the antiderivative of the answer is. Students answer correctly

- Introduce intergration by substitution. Students flail in confusion.

- Give students handy tips! If you see a something in parentheses, especially if it is raised to a power, multiplied by something else, you should expect to use substitution. If you see a bunch of stuff multiplied together, expect to use substitution. Let
*u* be the exponent on *e*. Let *u* be the denominator. Let *u* be something in parentheses raised to a power.

- Evaluate a derivative by the chain rule. Ask students what the antiderivative of the answer is. Students write down crazy shit involving
*u*.