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Question

Integrate:
x2(a+bx)2dx

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Solution

I=x2(a+bx)2dx

Let t=a+bxbdx=dt

I=(ta)2b2.t2dtb=1b3t2+a22att2dt

=1b3(1+a2t22at)dt

=1b3[ta2t2alog|t|]

I=1b3[(a+bx)a2(a+bx)2alog|bx+a|]+c

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