(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

[tex] \int \frac{1}{x(x^{2}+1)}dx[/tex]

2. Relevant equations

3. The attempt at a solution

well I split this into partial fractions

[tex] \frac{A}{x} + \frac{Bx + C}{x^{2} + 1}

so [tex] 1 \equiv A(x^{2}+1) + (Bx + C)x[/tex]

when x = 0, A =1

when x = 1, Bx + C = -1 so comparing coeffs tell us B = 0 and C = -1

Correct?

Now integrating it:

[tex] \int \frac{1}{x} - \frac{1}{x^{2} + 1}dx[/tex]

the first one is just ln |x|

and the second one

let [tex]u = x^{2} + 1[/tex]

u' = 2x

so

[tex] ln|x| - \int \frac{1}{2x u}du[/tex]

Have I gone wrong somewhere.

Thanks

Thomas

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# Homework Help: Partial fractions & Substitution Integration

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