Partial Fractions: find integral using given substitution

[chrisbush.sax]

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In the partial fractions chapter of my book, the question asks me to evaluate the given integral using the stated substitution:

integral sqrt((x-1)/(x+1))dx using u^2=(x-1)/(x+1)

so udu=dx/(x+1)^2

after that, I've tried direct subbing, rationalizing the square root, manipulating udu and u^2. But I still get a (x+1)^2 that I can't substitute for.

Any help is appreciated.

 

[Deleted member 4993]

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In the partial fractions chapter of my book, the question asks me to evaluate the given integral using the stated substitution:

integral sqrt((x-1)/(x+1))dx using u^2=(x-1)/(x+1)

so udu=dx/(x+1)^2

after that, I've tried direct subbing, rationalizing the square root, manipulating udu and u^2. But I still get a (x+1)^2 that I can't substitute for.

Any help is appreciated.

u² = 1 - 2/(x+1)

2/(x+1) = 1-u²

(x + 1)² = 4/(1-u²)² Now continue....