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int(1+x^(4))/((1-x^(4))^(3//2))dx is equ...

`int(1+x^(4))/((1-x^(4))^(3//2))dx` is equal to

A

`(x)/(sqrt(1-x^(4)))+C`

B

`(-x)/(sqrt(1-x^(4)))+C`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(1+x^(4))/((1-x^(4))^(3//2))dx`
`=int(x^(2)((1)/(x^(2))+x^(2)))/(x^(3)((1)/(x^(2))-x^(2))^(3//2))dx=int(((1)/(x^(3))+x))/(((1)/(x^(2))-x^(2))^(3//2))dx`
Put `(1)/(x^(2))-x^(2)=z`
`rArr" "((1)/(x^(3))+x)dx=-(dz)/(2)`
`therefore" "l=-(1)/(2)int(dz)/(z^(3//2))=z^(-1//2)+C=(x)/(sqrt(1-x^(4)))+C`
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