Integrating with Trigonometric Identities (Edexcel A-Level Mathematics): Flashcards

Use trigonometric identities to simplify first.

The integral is $-\cos(x) + C$.

The identity is $\sin^2\theta + \cos^2\theta \equiv 1$.

$\tan^2\theta + 1 \equiv \sec^2\theta$.

Integrate as $\sec^2\theta - 1$: $\tan\theta - \theta + C$.

Integrate to get $-\ln|\cos(\theta)| + C$.

Use the identity to get $-\frac{1}{4} \cos(2\theta) + C$.

Express as $1 - 2\sin^2\theta$.

Get $\frac{1}{2}\theta + \frac{1}{4} \sin(2\theta) + C$.

It's $\frac{1}{2}x - \frac{1}{8}\sin(4x) + C$.