MathAnalysisCalculusIntegrals

Further Integrals

Theory

Sine or Cosine?

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Which of the following is a solution to II?

I=∫1−sin⁡(x)(sec⁡(x)−tan⁡(x))2dxI = \int \frac{1 - \sin(x)}{(\sec(x) - \tan(x))^2} dxTip:

sec⁡(x)−tan⁡(x)=1−sin⁡(x)cos⁡(x)\sec(x) - \tan(x) = \frac{1-\sin(x)}{\cos(x)} and cos⁡2(x)=1−sin⁡2(x)=(1−sin⁡(x))(1+sin⁡(x))\cos^2(x) = 1 - \sin^2(x) = (1-\sin(x)) (1 + \sin(x))

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