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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int(x^(9)dx)/((4x^(2)+1)^(6))=int(dx)/(x^(3)(4+(1)/(x^(2)))^(6))`
`= -(1)/(2)int(d(4+(1)/(x^(2))))/((4+(1)/(x^(2)))^(6))= -(1)/(2)((4+(1)/(x^(2)))^(-5))/(-5)+C`
`=(1)/(10)(4+(1)/(x^(2)))^(-5)+C`
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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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