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Question

Integrate:
1(xa)(xb)dx

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Solution

I=dx(xa)(xb)

=dxx(xb)a(xb)=dxx2x(a+b)+ab

=dxx22(x)(a+b2)+ab=dx(xa+b2)2(ab2)2

log∣ ∣xa+b2+(xa+b2)2(ab2)2∣ ∣+c

=log∣ ∣xa+b2+x2x(a+b)+a2+b2+2ab4a2+b22ab4∣ ∣+c

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