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Let k(x)=int((x^2+1)dx)/(sqrt(x^3+3x+6))...

Let `k(x)=int((x^2+1)dx)/(sqrt(x^3+3x+6))a n dk(-1)=1/(3 3)` . Then the value of `k(-2)` is____

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The correct Answer is:
2
`k(x)=int((x^(2)+1)dx)/((x^(3)+3x+6)^(1//3))`
`"Put " x^(3)+3x+6=t^(3)`
`"or " 3(x^(2)+1)dx=3t^(2)dt`
`k(x)=int(t^(2)dt)/(t)=(t^(2))/(2)+C=(1)/(2)(x^(3)+3x+6)^(2//3)+C`
`k(-1)=(1)/(2)(2)^(2//3)+C " or " C=0`
` :. k(x)=(1)/(2)(x^(3)+3x+6)^(2//3),f(-2)=(1)/(2)(-8)^(2//3)`
`=(1)/(2)[(-2)^(3)]^(2//3)=2`
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