How do you integrate $[(x + 4)/(x^2 + 8 x +17)] dx$ ?

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Answer 1 · 2015-05-19T12:50:14

Use substitution:

$(x+4)/(x^2+8x+17) = (x+4)/(x^2+8x+16+1) = (x+4)/((x+4)^2+1)$

Now with $u=x+4$ this becomes $u/(u^2+1)$ whose integral (by another substitution) is

$1/2 ln (u^2+1) +C$

Finish by going back to the variable $x$ .

How do you integrate [(x + 4)/(x^2 + 8 x +17)] dx[(x + 4)/(x^2 + 8 x +17)] dx?