A calculus problem by Aareyan Manzoor

Calculus Level 4

Iy=23xy+1(x2+2xy+1)2dx\large I_y = \int_2^3 \dfrac{xy+1}{(x^2+2xy+1)^2} \, dx

Evaluate the integral above in terms of yy.

If I1=abI_1 = \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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