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Question

5x2+20x+6x3+2x2+x dx

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Solution

We have,I=5x2+20x+6x3+2x2+x=5x2+20x+6 dxx x2+2x+1=5x2+20x+6 dxx x+12Let 5x2+20x+6x x+12=Ax+Bx+1+Cx+125x2+20x+6x x+12=A x+12 +B x x+1+C xx x+125x2+20x+6=A x2+2x+1+B x2+x+Cx5x2+20x+6=A+B x2+2A+B+C x+AEquating coefficients of like termsA+B=5 .....12A+B+C=20 .....2 A=6 .....3Solving 1, 2 and 3, we getA=6 B=-1C=95x2+20x+6x x+12=6x-1x+1+9x+12I=6dxx-dxx+1+9dxx+12=6 log x-log x+1-9x+1+C

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