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Indefinite integral of simple trigonometric functions

Indefinite integral of simple trigonometric functions

IB Year 6 | Grade 12

Integrate the following with respect to \(x\):

  1. \( \displaystyle \displaystyle \displaystyle\int \sin\left(2x + \frac{\pi}{2}\right) \, \mathrm{d}x \)
  2. \( \displaystyle \displaystyle \displaystyle\int 6\sec^{2} 3x \, \mathrm{d}x \)
  3. \( \displaystyle \displaystyle \displaystyle\int \mathrm{cosec}\left(\frac{\pi}{4} - 3x\right)\cot\left(\frac{\pi}{4} - 3x\right) \, \mathrm{d}x \)

Solution:

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Answer:(a) \(-\frac12\cos\left(2x+\frac\pi2\right)+C_1\). (b) \(2\tan3x+C_2\). (c) \(\frac13\operatorname{cosec}\left(\frac\pi4-3x\right)+C_3\).

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