Question

integration of cos{2cot^-1 (√(1+x) /√(1-x) }dx​

Answer 1

abc's I am rejoining because I can't see the attached file is scanned image in PDF format to do it for the chai na kal isliye message was automatically generated by you against the spirit of fair play that all of the

Answer 2

$\sf∫ \cos( 2 \cot^{ - 1}{ ( \ \sqrt \frac{1 - x}{1 + x} ))dx}$

$\sf Let \: x = cosθ  \\ \\ \\ \sf dx = - sinθ \: dθ$

$\sf∫ \cos [2 \cot^{ - 1}( \sqrt \frac{1 - \cosθ}{1+ \cosθ} )] dθ$

$\sf \implies ∫ \cos[2 \cot^{ - 1} \: \{tan ( \frac{θ}{2}) \}]dθ$

$\sf \implies ∫ \cos[2 \cot^{ - 1} \{ \cot( \frac{\pi}{2} - \frac{θ}{2}) \}]dθ$

$\sf \implies ∫ \cos[2( \frac{\pi}{2} - \frac{θ}{2}) ]dθ$

$\sf \implies ∫ cos(π – θ) dθ$

$\sf \implies – ∫ cos(θ) dθ$

$\sf \implies – sinθ + c$

$\sf \implies – √(1 – x2) + c$