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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 (where C is a constant of integration)

A

`(-x^(5))/((x^(5)+x^(3)+1)^(2))+C`

B

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

C

`(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C`

D

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

Text Solution

Verified by Experts

Let `=int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1))dx` .Then,
`I=int((2)/(x^(3))+(5)/(x^(6)))/((1+(1)/(x^(2))+(1)/(x^(5)))^(3))dx` " " `["Dividing numerator and denominator by " x^(15)]`
`rArrI=-int(1)/((1+(1)/(x^(2))+(1)/(x^(5)))^(3))d(1+(1)/(x^(2))+(1)/(x^(5)))`
`rArrI=(1)/(2)(1+(1)/(x^(2))+(1)/(x^(5)))^(2)+C`
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