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"If " f(x)=int(dx)/(x^(1//3)+2) " and "f...

`"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2,` `" then the value of " f(-1) " is"-.`

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The correct Answer is:
7.5
`"Let " x=t^(3) `
` :. dx=3t^(2)dt`
` :.f(x)=int(dx)/(x^(1//3)+2)`
`=3int(t^(2)dt)/(t+2)`
`=3int((t^(2)-4+4)dt)/(t+2)`
`=3int(t-2+(4)/(t+2))dt`
`=3((t^(2))/(2)-2t+4log_(e)|t+2|)+c`
`=3((x^(2//3))/(2)-2x^(1//3)+4log_(e)|x^(1//3)+2|)+C`
`f(0)=12log_(e)2`
` :.c=0`
`:.f(-1)=(3)/(2)+6=(15)/(2)`
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