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Integrate.\newline cos⁡xsin⁡xcos⁡x \frac{\cos x \sin x}{\cos x}

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Full solution

Q. Integrate.\newline cos⁡xsin⁡xcos⁡x \frac{\cos x \sin x}{\cos x}
  1. Simplify integrand: Simplify the integrand cos⁡(x)sin⁡(x)/cos⁡(x)\cos(x) \sin(x)/\cos(x). cos⁡(x)sin⁡(x)/cos⁡(x)=sin⁡(x)⋅(cos⁡(x)/cos⁡(x))=sin⁡(x)⋅1=sin⁡(x)\cos(x) \sin(x)/\cos(x) = \sin(x) \cdot (\cos(x)/\cos(x)) = \sin(x) \cdot 1 = \sin(x)
  2. Integrate simplified integrand: Integrate the simplified integrand. ∫sin⁡(x) dx=−cos⁡(x)+C\int \sin(x) \, dx = -\cos(x) + C, where CC is the constant of integration.
  3. Check for errors: Check the result for any mathematical errors. The integration of sin⁡(x)\sin(x) is indeed −cos⁡(x)-\cos(x), and no mathematical errors are present in the calculation.

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