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Evaluateint(x^3)/(x^4+3x^2+2) dx...

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

Text Solution

Verified by Experts

Let,I= `int(x^3)/(x^4+3x^2+2) dx`
Let `x^2=t`
`2xdx=dt`
So,I=`int(x^3)/(x^4+3x^2+2) dx`
=`1/2(tdt)/((t+2)(t+1))`
=`1/2int(2/(t+2)-1/(t+1))dt`
=`1/2(2log(t+2)-log(t+1))+C`
=`log((t+2)/sqrt(t+1))`
...
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