Integration of Rational Functions By Partial Fractions

**HellaciousD** · October 2nd 2008, 05:57 PM

Hello all,

I am trying to integrate (3x^2+7x+3)/(x^2+1)^2
I am down to the integral of (3/(x^2+1))+ the integral of (7x/(x^2+1)^2)+ the integral of (3/(x^2+1)^2) and I don't really know what to do
I believe the next step starts with arctan(3x) but then I don't know what to do with the other stuff.

Thanks,
Jay

**Nacho** · October 2nd 2008, 06:13 PM

$ \int {\frac{{3x^2 + 7x + 3}} {{\left( {x^2 + 1} \right)^2 }}dx} = \int {\frac{{3x^2 + 3}} {{\left( {x^2 + 1} \right)^2 }}dx + \int {\frac{{7x}} {{\left( {x^2 + 1} \right)^2 }}dx} } = $

$ 3\int {\frac{1} {{x^2 + 1}}dx} + 7\int {\frac{x} {{\left( {x^2 + 1} \right)^2 }}dx} $

$ \begin{gathered} u = x^2 + 1 \Rightarrow du = 2xdx \hfill \\ \hfill \\ = 3\arctan x + \frac{7} {2}\int {\frac{1} {{u^2 }}du = } 3\arctan x + \frac{7} {2} \cdot \frac{{u^{ - 2 + 1} }} {{ - 2 + 1}} \hfill \\ \end{gathered} $

$ = \boxed{3\arctan x + \frac{7} {2} \cdot \frac{1} {{x^2 + 1}}} $

I forget the integration constant :P

**HellaciousD** · October 2nd 2008, 06:21 PM

Thanks, but the program I'm using isn't accepting that answer. Are you sure it's right?
Jay

**Nacho** · October 2nd 2008, 06:25 PM

Originally Posted by HellaciousD

Thanks, but the program I'm using isn't accepting that answer.
Jay

look that I make a mistake in a sign, before 7/2... should to have a "-"

sorry

**HellaciousD** · October 2nd 2008, 07:20 PM

Can someone tell me why the integral of 32dx/(x(x^2+4)^2) doesn't come out to 2ln(abs(x))?

Thanks,
Jay

Thread: Integration of Rational Functions By Partial Fractions

LinkBack

Thread Tools

Display

Integration of Rational Functions By Partial Fractions

Similar Math Help Forum Discussions

Long division! intregration of rational functions by partial fractions

Integration by partial fractions

Integration of Rational Functions By Partial Fractions

Integration of Rational Functions by Partial Fractions

Integration of Rational Functions by partial fractions

Search Tags