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Evaluate: int(x^3)/(x^4+3x^2+2)dx...

Evaluate: `int(x^3)/(x^4+3x^2+2)dx`

Text Solution

Verified by Experts

I=`int(x^3)/(x^4+3x^2+2)dx`
let `x^2=t`
`2xdx=dt`
So,
`I=1/2int (tdt)/((t+2)(t+1))`
`I=1/2 int ([2/(t+2)-1/(t+1)]dt)`
`I=1/2(2log(t+2)-log(t+2))+c`
`I=1/2(2log(x^2+2)-log(x^2+2))+c ...
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