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## Homework Statement

I=∫cot(x)dx

## Homework Equations

wht's wrong in this approach (integrating by parts)

## The Attempt at a Solution

I=∫cot(x)dx=∫[itex]\frac{cos(x)}{sin(x)}[/itex]dx=∫[itex]\frac{-(sin(x))'}{sin(x)}[/itex]=[itex]\frac{-sin(x)}{sin(x)}[/itex]-∫-sin(x)([itex]\frac{1}{sin^2(x)}[/itex])'dx=-1+∫sin(x)[itex]\frac{-cos(x)}{(sin(x))^2}[/itex]=-1-∫[itex]\frac{cos(x)}{sin(x)}[/itex]

⇔I+C=-1-I⇔I=-[itex]\frac{1}{2}[/itex] → I=C

_{1}??

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