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If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x...

If `int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e nai se q u a l` `1/3` (b) `2/3` (c) `-1/3` (d0 `-2/3`

A

`1//3`

B

`2//3`

C

`-1//3`

D

`-2//3`

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `1-x^(3)=y^(3), -3x^(2)dx=2y dy,` we get
`int (1)/(xsqrt(1-x^(3)))dx= -(2)/(3) int (1)/(1-y^(2))dy`
`=(1)/(3)log|(y-1)/(y+1)|+C`
`=(1)/(3)log |(sqrt(1-x^(3))-1)/(sqrt(1-x^(3))+1)|+C " or " a=(1)/(3)`
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