Read the Structure, Then Choose

You'll learnto run four questions in order over an integrand nobody has labeled, to read the structural tell that decides between rewriting, substitution and parts, and to settle every answer in seconds by differentiating what you wrote.

Every technique in this unit is now available and no new one is coming. What is new is that nobody tells you which one to use, and two integrands that call for different methods can differ by a single symbol. So the skill stops being a procedure and becomes a reading: what is inside what, whose derivative is present, which two pieces are unlike each other. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · READ THE STRUCTURE, THEN DIFFERENTIATE THE ANSWER · v2

Read the structure, choose the technique, then differentiate the answer

Before you start

What you're looking at

One plot. The blue curve is the integrand; the yellow dashed curve is the measured slope of a candidate answer, and a red one is a wrong answer's slope.

The question

With every technique available and none of them labeled, how do you tell from the integrand alone which one to reach for?

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