Techniques of Integration - Integrating Powers of Sine and Cosine

Techniques of Integration - Integrating Powers of Sine and Cosine

Integrate the following expressions with respect to \(x\).

  1. \(\displaystyle\displaystyle \displaystyle\int \cos^2 (5x) - 1\, \mathrm{d}x\)
  2. \(\int2 - \sin^2 (3x) \, \mathrm{d}x\)
  3. \(\displaystyle\displaystyle \displaystyle\int \tan^2 (3x) \, \mathrm{d}x\)

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Answer:(a) \(\frac1{20}\sin10x-\frac12x+C\). (b) \(\frac32x+\frac1{12}\sin6x+C\). (c) \(\frac13\tan3x-x+C\).

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