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`int(1)/((x-1)sqrt(x^(2)-1))dx` equalsA. `-sqrt((x-1)/(x+1))+C`B. `sqrt((x-1)/(x+1))+C`C. `sqrt((x+1)/(x-1))+C`D. `-sqrt((x+1)/(x-1))+C` |
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Answer» Correct Answer - d Let `I=int(1)/((x-1)sqrt(x^(2))-1)dx=int(1)/((x-1)^(3//2)sqrt(x+1))dx` `rArrI=int((x+1)/(x-1))^(3//2)(1)/((x+1)^(2))dx=(1)/(2)int((x-1)/(x+1))^(-3//2)d((x-1)/(x+1))` `rArrI=-((x-1)/(x+1))^(-1//2)+C=-sqrt((x+1)/(x-1))+C` |
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