Pure · Integration
Chapter 1 · 3
The idea
Integrating with trigonometric identities
Integrals like sin²x, cos²x and tan²x that have no direct rule — rewritten with the double-angle and Pythagorean identities into things you can integrate term by term.
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Pure · Integration
Integrating with trigonometric identities
Integrals like sin²x, cos²x and tan²x that have no direct rule — rewritten with the double-angle and Pythagorean identities into things you can integrate term by term.
Why it works
No table entry for sin²
Find . There is no entry in the integral table for , and the tempting guess fails: the answer is not , because differentiating that gives — the chain rule leaves a the guess forgot. Nothing in the table will ever match a squared trig function directly. The way through — and the whole method of this lesson — is to rewrite the integrand with a trig identity until every term is something the table does contain. By the end of the next section, the opening integral will be two lines long.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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