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

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

Text Solution

Verified by Experts

I=`int(x^3-3x)/(x^4+2x^2-4)\ dx`
=`1/2int(2x)(x^3-3x)/(x^4+2x^2-4)\ dx`
Let `x^2=t⇒2xdx=dt`
=`1/2int(t-3)/(t^2+2t-4)\ dx`
=`1/4int(2t-6)/(t^2+2t-4)\ dx`
=`1/4int(2t+2-8)/(t^2+2t-4)\ dx`
=`1/4int(2t+2)/(t^2+2t-4)\ dx-2int1/(t^2+2t-4)dx`
=`1/4int(2t+2)/(t^2+2t-4)\ dx-2int1/((t+1)^2−(sqrt(5))^2​)dt`
...
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