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integrate of (x^4 + 1)/(x^2 + 1) dx is
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\[(x^4+1)(x^2+1)= x^6+x^4+x^2+1\] i have used law of distribution ..now you can integrate easily
i not multiply, it's divide.
\[\frac{x^4+1}{x^2+1}=\frac{x^4-1+2}{x^2+1}=\frac{(x^2-1)(x^2+1)+2}{x^2+1}\]make sense?
so, how to integrate 2/(x^2 + 1) dx ?
first long division. then use Partial fractions.
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How do you integrate 1/(x^2+1)?
This is a memory thing. Or you could go the long way and get it .
d/dx (arctan(x)=1/(1+x^2)
i stil don't understand
\[\frac{ d }{ dx }(\tan^{-1}x)= \frac{ 1 }{ 1+x^2 }\]
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\[\int\limits_{?}^{?} (\frac{ 1 }{ 1+x^2 })= \tan^{-1}x\]
ok, thx for your help, i so appreciate :)
:)
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