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How do you integrate $\int (\frac{cos (x)}{sin (x)} - 1) d x$ $int (cos(x)/sin(x)-1)dx$ ?

1 Answer

Feb 7, 2016

$ln | sin x | - x + C$ $ln|sinx|-x+C$

Explanation:

$\int (\frac{cos x}{sin x} - 1) d x = \int (cot x - 1) d x$ $int(cosx/sinx-1)dx=int(cotx-1)dx$

$= \int cot x d x - \int d x$ $=intcotxdx-intdx$

$= ln | sin x | - x + C$ $=ln|sinx|-x+C$

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