Integration of (5x+4)÷(x2+3x+2)1/2

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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

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