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"If " int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3...

`"If " int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3)+2x)dx=f(x)+C, " then the value of " f(1)xxf(-1) " is"-.`

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The correct Answer is:
1
`int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3)+2x)dx`
`=int underset(I)(underbrace(x^(2)))underset(II)(underbrace(e^(x^(3)+x^(2)-1)(3x^(2)+2x)))dx+int e^(x^(3)+x^(2)-1)2x dx`
`=x^(2)e^(x^(3)+x^(2)-1)-int 2xe^(x^(3)+x^(2)-1)dx+int e^(x^(3)+x^(2)-1) 2xdx`
`=x^(2)e^(x^(3)+x^(2)-1)+C`
`implies f(1)=e " and " f(-1)=(1)/(e)`
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