- #1
Screwdriver
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Homework Statement
Well gentlemen, another year, another integral eh? Anyways,
[tex]\int \frac{1}{x^4+4}\,dx[/tex]
I really want to do this without looking at Wolfram/Google.
Homework Equations
U-substitutions, parts, partial fractions
The Attempt at a Solution
Basically I tried to factor the denominator and then subtract something to make up the difference:
[tex]\int \frac{1}{x^4+4}\,dx = \int \frac{1}{(x^2 + 2)^2 - 4x^2}\,dx[/tex]
Then I also noticed that:
[tex]\int \frac{1}{(x^2 + 2)^2 - 4x^2}\,dx = \int \frac{1}{(x^2 + 2)^2 - (2x)^2}\,dx[/tex]
Now here's the iffy part; I know that
[tex]\frac{1}{(x^2 + 2)^2 - (2x)^2} \neq \frac{1}{(x^2 - 2x + 2)^2}[/tex]
But I feel like If I can somehow combine those two things I can maybe decompose this into partial fractions. Yay or nay?