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int(x^9)/((4x^2+1)^6) dx is equal to...

`int(x^9)/((4x^2+1)^6) dx` is equal to

A

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

B

`(1)/(5)(4+(1)/(x^(2)))^(-5)+C`

C

`(1)/(10x)(1+4)^(-5)+C`

D

`(1)/(10)((1)/(x^(2))+4)^(-5)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `" "l=int(x^(9))/((4x^(2)+1)^(6))dx`
`=int(x^(9))/(x^(12)(x+(1)/(x^(2)))^(6))dx=int(1)/(x^(3)(4+(1)/(x^(2)))^(6))dx`
`"Put "4+(1)/(x^(2))=t rArr -(2)/(x^(3))dx=dt`
`rArr" "(dx)/(x^(3))=-(1)/(2)dt therefore l=-(1)/(2)int(dt)/(t^(6))`
`l=-(1)/(2)xx(t^(-5))/(-5)+C rArr l=(1)/(10) t^(-5)+C`
`l=(1)/(10)((1)/(x^(2))+4)^(-5)+C`
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