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Question

6x217x5(x3)(x2)2dx=

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Solution

6x217x5(x3)(x2)2dx
Let 6x217x5(x3)(x2)2=Ax3+B(x2)+C(x2)2
6x217x5=A(x2)2+B(x3)(x2)+C(x3)
=A(x24x+4)+B(x25x+6)+C(x3)
Comparing Coefficients,
A+B=6
4A5B+C=17
4A+6B3C=5
A=2,B=8,C=15
6x217x5(x3)(x2)2dx=(2x3+8x2+15(x2)2)dx
=2log|x3|+8log|x2|15(x2)+C

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