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If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^...

If `I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C`, then f(x) is equal to

A

`(x^(4)(1+x+x^(2))^(7))/(7)+C`

B

`(x^(28)(1+x+x^(2))^(7))/(7)+C`

C

`(x^(28)(1+x+x^(2))^(7))/(28)+C`

D

None

Text Solution

Verified by Experts

The correct Answer is:
B
`I=intx^(24)(1+x+x^(2))^(6).{x^(3)(4+5x+6x^(2))}dx`
`=int(x^(4)+x^(5)+x^(6))^(6).(6x^(5)+5x^(4)+4x^(3))dx`
`=(x^(28)(1+x+x^(2))^(7))/(7)+c`
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