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

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

Text Solution

Verified by Experts

I=`int(x+1)/(x^2+x+3)dx`
Let `u=x^2+2x+3.`
Then `du=(2x+2)dx, so 1/2du=(x+1)dx`
Thus,`int1/2 du/u`
=`1/2(ln(|u|)+C)`
=`1/2(ln(|x^2+2x+3|)+C)`
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