# Evaluate the following integrals: Consider Expressing the integral   Consider Let and split,  Consider Let   We know that  Now consider  By partial fraction decomposition, 1 = A (x – 2) + B (x – 3)

1 = Ax – 2A + Bx – 3B

1 = (A + B) x – (2A + 3B)

A + B = 0 and 2A + 3B = -1

Solving the two equations,

2A + 2B = 0

2A + 3B = -1

-B = 1

B = -1 and A = 1  Consider Let u = x – 3 dx = du We know that  Similarly Let u = x – 2 dx = du We know that  Then,  Then,   Then, We know that     Rate this question :

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