Question

ſ cot^-1 (cosec x + cot x) dx​

Answer 1

Answer:

Simply

$\frac{1 }{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } = \frac{1 + \cos(x) }{ \sin(x) } = \frac{2 \cos {}^{2} ( \frac{x}{2} ) }{2 \sin( \frac{x}{2} ) \cos( \frac{x}{2} ) } = \cot( \frac{x}{2} )$

So integral nothing but

$\int \cot {}^{ - 1} ( \cot( \frac{x}{2} ) ) dx = \int \frac{x}{2} dx = \frac{ {x}^{2} }{4} + c$

Answer 2

Answer:

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