Results 1 to 4 of 4

Math Help - partial fractions

  1. #1
    Member
    Joined
    Nov 2005
    Posts
    172

    partial fractions

     \int\frac{x^2-x+1}{x^3+x}dx

    \frac{x^2-x+1}{x(x^2+1)} = \frac{A}{x}+\frac{Bx+C}{x^2+1}

    x^2-x+1 = A(x^2+1)+(Bx+C)X

    i plugged in  x=0 and got A=1
    need help finding  B and  C
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    No, not quite. You got mixed up with (x^{2}+1)^2

    \frac{x^{2}-x+1}{x(x^{2}+1)}

    \frac{A}{x}+\frac{B}{x^{2}+1}=x^{2}-x+1

    Now continue.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    If you prefer, partial fractions can be avoid

     <br />
\begin{aligned}<br />
\int\frac{x^2-x+1}{x^3+x}~dx&=\int\frac{(x^2+1)-x}{x^3+x}~dx\\<br />
&=\int\frac1{x}~dx-\int\frac1{1+x^2}~dx\\<br />
&=\ln|x|-\arctan{x}+k,\color{blue}~k\in\mathbb{R}<br />
\end{aligned}<br />

    I think partial fractions technique shoul be used if the problem really needs it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Yes, I agree with Krizalid. Like the 'Hospital' rule. If I can, I prefer to evaluate limits without it first.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 28th 2010, 10:53 AM
  2. Partial Fractions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 4th 2010, 07:24 PM
  3. Partial Fractions
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: January 17th 2010, 03:20 AM
  4. Help on Partial Fractions
    Posted in the Calculus Forum
    Replies: 12
    Last Post: January 6th 2010, 04:00 AM
  5. partial fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 21st 2007, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum