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

B

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

C

`ln|x^(5)+x^(3)+1|+sqrt((2x^(7)+5x^(4)))+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx=int(((2)/(x^(3))+(5)/(x^(6))))/(1+(1)/(x^(2))+(1)/(x^(5)))^(3)dx`
`"Put "1+(1)/(x^(2))+(1)/(x^(5))=t`
`therefore" "(-(2)/(x^(3))-(5)/(x^(6)))dx=dt`
`"Then, "l=-int(dt)/(t^(3))=(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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