If int x^(26).(x-1)^(17).(5x-3)dx=(x^(27...

If `int x^(26).(x-1)^(17).(5x-3)dx=(x^(27).(x-1)^(18))/(k)+C` where C is a constant of integration, then the value of k is equal to

A

3

B

6

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:

C

Differentiating both sides gives
`x^(26).(x-1)^(17)(5x-3)=(1)/(k)[x^(27).18(x-1)^(17)+(x-1)^(18)27x^(26)]`
`=(x^(26)(x-1)^(17))/(k)[18x+27(x-1)]`
`=(x^(26)(x-1)^(17))/(k)(45x-27)`
`=9(x^(26)(x-1)^(17))/(k)(5x-3)`
`rArrk=9`

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