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Misc integral

  • Thread starter nameVoid
  • Start date
  • #1
241
0
[tex]
\int \frac{dx}{x(x^4+1)}
[/tex]
[tex]
u=x^2
[/tex]
[tex]
\sqrt{u}=x
[/tex]
[tex]
dx=\frac{1}{2\sqrt{u}}
[/tex]
[tex]
\frac{1}{2}\int \frac{du}{u^2+1}
[/tex]
[tex]
\frac{1}{2}arctanx^2+C
[/tex]

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
33,503
5,191
[tex]
\int \frac{dx}{x(x^4+1)}
[/tex]
[tex]
u=x^2
[/tex]
[tex]
\sqrt{u}=x
[/tex]
[tex]
dx=\frac{1}{2\sqrt{u}}
[/tex]
[tex]
\frac{1}{2}\int \frac{du}{u^2+1}
[/tex]
The integral above isn't right. You forgot to replace the x factor in the denominator.
[tex]
\frac{1}{2}arctanx^2+C
[/tex]

Homework Statement





Homework Equations





The Attempt at a Solution

 
  • #3
241
0
[tex]
\frac{1}{2} \int \frac{du}{u(u^2+1)}=\int \frac{A}{u}+\frac{Bu+C}{u^2+1}du
[/tex]
[tex]
A=\frac{1}{2}=-B
[/tex]
[tex]
ln|x|-\frac{1}{4}ln(x^4+1)+C
[/tex]
 

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