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Question

The value of (x1)(x2)(x3)(x4)(x5)(x6) dx is
(where C is the constant of integration)

A
x+3ln|x4|24ln|x5|+30ln|x6|+C
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B
x+3ln|x4|12ln|x5|+30ln|x6|+C
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C
x+3ln|x4|12ln|x5|+36ln|x6|+C
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D
x+12ln|x4|24ln|x5|+30ln|x6|+C
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Solution

The correct option is A x+3ln|x4|24ln|x5|+30ln|x6|+C
I=(x1)(x2)(x3)(x4)(x5)(x6)dx
=[1+(x1)(x2)(x3)(x4)(x5)(x6)1]dx
=[1+(x1)(x2)(x3)(x4)(x5)(x6)(x4)(x5)(x6)]dx
=[1+3×2×1(x4)(1)(2)+4×3×2(1)(x5)(1)+5×4×3(2)(1)(x6)]dx
=[1+3(x4)24(x5)+30(x6)]dx
=x+3ln|x4|24ln|x5|+30ln|x6|+C

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