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If 1 [5](x - 1)4(x + 3)6 dx = A ( x - 1 x + 3 )B + C, where C is the constant of integration, then the value of + + 20AB is .
7
I = dx(x - 1)4/5(x + 3)6/5
= ( x - 1x + 3 )-4/5 dx(x + 3)2
Put x - 1x + 3 = t 4(x + 3)2 dx = dt
I = 14 t-4/5 dt = 54t1/5 + C
= 54 ( x - 1x + 3 )1/5 + C
A = 54, B = 15, = = 1
∴ + + 20AB = 2 + 20 54 15 = 7
Answer: 7
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