Integration by Partial Fraction

• Find the value of the constant a,b,c,d,e,f,g,h,i, and j.
• Show the complete solution.
• 

x3+ 2x 2 + 4 B ( x-3 ) 4 ( x - 2) 2 ( x 2 + 2 x+5 ) = . A + C D E X - 3 (x - 3) ( x- 3 ) 3 + ( x - 3 ) 4 + + F X - 2 Gx + H Ix + J x 2 + 2x +5 ( x 2 + 2 x + 5) 2 ( x - 3 ) " ( x - 2 ) 2 ( x 2 + 2 x + 5 ) 2@ X ": 0 = At E + G @ x8 : 0 = - 9A + B - 10E+F - 14G + H @ X" : 0 = 29A - 6B + C + 36E- 8F + 79G- 14H+I C x": 0 = - USA + 11 B - 3C + D - 80E + 20 F - 240 G + 79 H - lu It J @ x5 : 0 = 23SA - 32B + 2C+ 270 E- 40F + 525G -240H + 106I-16J @x":0 = - 623A + 439B - 26C+20 - 788 E+ 190F - 1158 6 + 515H - 3721 +1065 @ x3 : 1 = 847A - 206B+ 61C-200 +1140E - 408F+ 245+G- 1158H + 729 1-372J @ * 2 : 2 = - 1467A + 219 B - 23 C + D - 1728 E + 324 F - 3132 G + 2457H - 756 I+ 729 J @x': 0 = 3240A - 780B+160C - 20D + 4185 E - 1080F + 1620 G - 3132 H + 3241-756J @ x: 4 = - 2700 A + 900B - 300C + 1000 - 40 50 E + 2025 F + 1620 H + 324 J