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Question

2(x31)x3(2x+1x2)dx, x>1 is equal to -
  1. ln(2x+1x2)+c
  2. ln(2x3+1)+c
  3. tan1(1x32+1)+ln(x1x+1)+c
  4. ln(x+x1x+1)+c


Solution

The correct option is A ln(2x+1x2)+c
2(x31)x3(2x+1x2)dx

2x+1x2=t(22x3)dx=dt

dtt=ln|t|+c=ln(2x+1x2)+c

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