Please can you explain this integration result?
- Thread starter val1
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pka
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- Jan 29, 2005
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The antiderivative is done with partial fractions.
\(\displaystyle \L
\frac{1}{{y^2 - 1}} = \frac{1}{{2\left( {y - 1} \right)}} - \frac{1}{{2\left( {y + 1} \right)}}\)
Look at the derivative of your function:
\(\displaystyle \L
y = \frac{1}{2}\ln (y^2 - 1)\quad \Rightarrow \quad y' = \frac{y}{{y^2 - 1}}\)
\(\displaystyle \L
\frac{1}{{y^2 - 1}} = \frac{1}{{2\left( {y - 1} \right)}} - \frac{1}{{2\left( {y + 1} \right)}}\)
Look at the derivative of your function:
\(\displaystyle \L
y = \frac{1}{2}\ln (y^2 - 1)\quad \Rightarrow \quad y' = \frac{y}{{y^2 - 1}}\)