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The integral int(2x^(12)+5x^(9))/((x^(5)...

The integral `int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))` dx is equal to

A

`(x^(10))/(2(1+x^(3)+x^(5))^(4))+c`

B

`(x^(2)+2x)/((x^(5)+x^(3)+1)^(4))+c`

C

`(x^(10))/(2(x^(5)+x^(3)+1)^(2))+c`

D

`(2x^(10))/((x^(5)+x^(3)+1)^(3))+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx`
`=int (((2)/(x^(3))+(5)/(x^(6)))dx)/((1+(1)/(x^(2))+(1)/(x^(5)))^(3))`
`=int (-dt)/(t^(3)), " where " t=1+(1)/(x^(2))+(1)/(x^(5))`
`=(1)/(2t^(2))+C`
` =(1)/(2(1+(1)/(x^(2))+(1)/(x^(5)))^(2))+c`
`=(x^(10))/(2(x^(5)+x^(3)+1)^(2))+c`
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