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Integrate sqrt( (1+x)/(1-x))?

+1 vote
please help
asked Feb 19, 2013 in CALCULUS by futai Scholar

1 Answer

+2 votes

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Multiply nominator and denominator by √(1+x)

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answered Feb 22, 2013 by britally Apprentice

Find ʃ [ (x dx)/√(1 - x2) ].

Let (1 - x2) = u2  ⟹  u = √(1 - x2)

Apply derivative to each side.

- 2x dx = 2u du   ⟹  x dx = - u du.

ʃ [ (x dx)/√(1 - x2) ]  = ʃ [ (- u du)/u ] = - ʃ 1 du = - u + C= - √(1 - x2) + C.

The final solution ʃ √[ (1 + x)/(1 - x) ] dx = sin- 1 (x) - √(1 - x2) + C.

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