Integration - Integrable Forms of Trigonometric Functions
Integration - Integrable Forms of Trigonometric Functions
IB AA SL: core and optional content
Core: parts (b) and (c), sine, cosine and power integrals. Optional: part (a), which rewrites as an integral of sec².
Integrate the following expressions with respect to \(x\).
- \(\frac{\tan^2 2x(4\sin^2 2x-1)}{\sin^2 2x}\)
- \(\sin\left(\frac{\pi+x}{4}\right)-4x^3+5\)
- \(\pi \cos \left( \frac{\pi x-1}{3} \right)\)
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Answer:(a) \(\frac32\tan2x-4x+C\). (b) \(-4\cos\left(\frac{\pi+x}{4}\right)-x^4+5x+C\). (c) \(3\sin\left(\frac{\pi x-1}{3}\right)+C\).
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