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Evaluate: int(5x-2)/(1+2x+3x^2)dx...

Evaluate: `int(5x-2)/(1+2x+3x^2)dx`

Text Solution

Verified by Experts

I=`int(5x-2)/(1+2x+3x^2)dx`
=`5/6int(6x-12/5)/(1+2x+3x^2)dx`
I=`5/6int(6x-12/5+2-2)/(1+2x+3x^2)dx`
I=`5/6[int(6x+2)/(1+2x+3x^2)dx-22/5int(3)/(3+6x+9x^2)dx]`
Let `1+2x+3x^2=t`
⇒`(6x+2)dx=dt`
...
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