If f3x−43x+4=x+2, then ∫f(x)dx is equal to

If f3x43x+4=x+2, then f(x)dx is equal to

  1. A

    ex+2loge3x43x+4

  2. B

    83loge|1x|+23x+C

  3. C

    83logt|x1|+x3+C

  4. D

    none of the

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    Solution:

    We have, f3x43x+4=x+2

    Let 3x43x+4=α

     (3x4)+(3x+4)(3x4)(3x+4)=α+1α1 6x8=α+1α1 x=43α+1α1 x+2=4α+43α3+2=4α4+6α63α3=2α103α3 f3x43x+4=x+2 f(α)=2α103α3

    f(α)=23α5α1f(α)=23α14α1=2314α1=2383(α1)f(x)=2383(x1)f(x)dx=2383(x1)dxf(x)dx=23x83loge|x1|+C

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