Integration of (5x+4)÷(x2+3x+2)1/2

Dear Student,
Please find below the solution to the asked query:

We have:I=5x+4x2+3x+2.dxTry to create derivative of x2+3x+2 i.e ddxx2+3x+2=2x+3, in thenumerator.5x+4x2+3x+2.dx=5x+45x2+3x+2.dx=522x+85x2+3x+2.dx Multiply and divide by 2=522x+3+85-3x2+3x+2.dx=522x+3-75x2+3x+2.dxI=522x+3x2+3x+2.dx-751x2+3x+2.dx ;iLet J=2x+3x2+3x+2.dxSet x2+3x+2=t2x+3.dx=dtJ=dtt=2t=2x2+3x+2Let K=1x2+3x+2.dx=1x+322-94+2.dx=1x+322-14.dx=1x+322-122.dx=lnx+32-x+322-212K=lnx+32-x2+3x+2Put value of J and K in iI=522x2+3x+2-75lnx+32-x2+3x+2+C


Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 1
What are you looking for?