Techniques of Integration - Integrating Powers of Sine and Cosine

IB AA SL: core and optional content

Core: the third integral, involving sin²(2x)+cos²x. Optional: the first two integrals involving sec.

Integrate the following expressions with respect to \({x}\)

1. \(3\sec^2 4x + \sin 3x\)
2. \(6 \cos 2x - \sec^2 2x + \sqrt{x}\)
3. \(\sin^2 2x + \cos^2 x\)