# integration partial fractions

• Jun 6th 2008, 09:40 AM
khuezy
integration partial fractions
integral of (u+4)/((u^2)+4) du

How would I solve for this?
• Jun 6th 2008, 09:43 AM
Mathstud28
Quote:

Originally Posted by khuezy
integral of (u+4)/((u^2)+4) du

How would I solve for this?

THere is no need for partial fractions here

$\int\frac{u+4}{u^2+4}du=\int\frac{u}{u^2+4}du+4\in t\frac{du}{u^2+4}=\frac{1}{2}\ln|u^2+4|+2\arctan\b igg(\frac{u}{2}\bigg)+C$

Also, conider the fact that if you wanted to do this by partial fractions the denominators factorization would be imaginary

And even if it is too hard to learn LaTeX a useful command is alt 0178 gives ²
• Jun 6th 2008, 09:57 AM
Krizalid
Since $u^2+4$ is positive for all $u,$ we can remove the absolute value bars.
• Jun 6th 2008, 09:58 AM
Mathstud28
Quote:

Originally Posted by Krizalid
Since $u^2+4$ is positive for all $u,$ we can remove the absolute value bars.

Thanks Krizalid, that is a good point. I just automatically did it...better than what I usually do and don't put them at all (Cool)