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Evaluate : int(2x)/((1-x^2)sqrt(x^4-1))d...

Evaluate : `int(2x)/((1-x^2)sqrt(x^4-1))dx`

Text Solution

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`int (2x)/((1-x^(2))sqrt(x^(4)-1))dx=int (-2x)/((x^(2)-1)^(3//2)sqrt(x^(2)-1))dx`
Put `sqrt((x^(2)+1)/(x^(2)-1))=z`
` :. (1)/(2)((x^(2)+1)/(x^(2)-1))^(1//2)((x^(2)-1)2x-(x^(2)+1)2x)/((x^(2)-1)^(2))dx=dz`
or `(sqrt(x^(2)-1))/(sqrt (x^(2)+1))(-2x)/((x^(2)-1)^(2))dx=dz`
or `(-2x)/((x^(2)-1)^(3//2)sqrt(x^(2)+1))dx=dz`
` :. " Given integral "= int dz=z+c=sqrt((x^(2)+1)/(x^(2)-1))+c`
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