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int(x+1)(x+2)^7(x+3)dx is equal to...

`int(x+1)(x+2)^7(x+3)dx` is equal to

A

`((x+2)^(10))/(10)-((x+2)^(8))+C`

B

`((x+1)^(2))/(2)-((x+2)^(8))/(8)-((x+3)^(2))/(2)+C`

C

`((x+2)^(10))/(10)+C`

D

`((x+1)^(2))/(2)+((x+2)^(8))/(8)+((x+3)^(2))/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `(x+1)(x+3)=(x+2-1)(x+2-1)`
`=(x+1)^(2)-1`
`therefore int(x+1)(x+2)^(7)(x+3)dx=int{(x+2)^(9)-(x+2)^(7)}dx=((x+2)^(10))/(10)-((x+2)^(8))/(8)+C`
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