If `f((3x-4)/(3x+4))=x+2`, then `int` f(x)dx is equal toA. `e^(x+2)log_(e)|(3x-4)/(3x+4)|`B. `-(8)/(3)log_(e)|1-x|+(2)/(3)x+C`C. `(8)/(3)log_(e)|x-1|+(x)/(3)+C`D. none of these

If `f((3x-4)/(3x+4))=x+2`, then `int` f(x)dx is equal toA. `e^(x+2)log

1.	If `f((3x-4)/(3x+4))=x+2`, then `int` f(x)dx is equal toA. `e^(x+2)log_(e)\|(3x-4)/(3x+4)\|`B. `-(8)/(3)log_(e)\|1-x\|+(2)/(3)x+C`C. `(8)/(3)log_(e)\|x-1\|+(x)/(3)+C`D. none of these
Answer» Correct Answer - b We have , `f((3x-4)/(3x+4))=x+2` Let `(3x-4)/(3x+4)=alpha` ` rArr ((3x-4)+(3x+4))/((3x-4)-(3x+4))=(alpha+1)/(alpha-1)` `rArr(6x)/(-8)=(alpha+1)/(alpha-1)` `rArrx=-(4)/(3)((alpha+1)/(alpha-1))` `rArrx+2=-(4alpha+4)/(3alpha-3)+2=(-4alpha-4+6alpha-6)/(3alpha-3)=(2alpha-10)/(3alpha-3)` `becausef((3x-4)/(3a+4))=x+2` `rArrf(alpha)=(2alpha-10)/(3alpha-3)` `rArrf(alpha)=(2)/(3)((alpha-5)/(alpha-1))` `rArrf(alpha)=(2)/(3)((alpha-1-4)/(alpha-1))=(2)/(3)(1-(4)/(alpha-1))=(2)/(3)-(8)/(3(alpha-1))` `rArrf(x)=(2)/(3)-(8)/(3(x-1))` `rArr intf(x)dx=int{(2)/(3)-(8)/(3(x-1))}dx` `becauseintf(x)dx=(2)/(3)x-(8)/(3)log_(e)\|x-1\|+C`

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