Here's the question you clicked on:
RolyPoly
Differential equation Did I make any mistakes here? \[\frac{dx}{dt} - x^3 = x\]\[\frac{dx}{dt} = x^3 + x\]\[\frac{dx}{x^3+x} = dt\]\[(\frac{1}{x}- \frac{x}{x^2+1})dx = dt\]\[\ln |x| - tan^{-1}x = t + c\]
\[\frac{ dx }{ x^3+1 }=dt\] Hmm why isn't it equal to this? :o Maybe I'm missing something.\[\frac{ dx }{ x^3+x }=dt\]
Ah ok i thought so :) imma check the fraction decomp a sec
\[\int\limits_{}^{}\frac{ 1 }{ x^2+1 }dx=\tan^{-1}x\] \[\int\limits_{}^{}\frac{ x }{ x^2+1 }dx \neq \tan^{-1}x\] Woops! That's just another natural log I think! :o
Oops! The problem is the partial fraction!!
It is? Hmm I got the same thing you did...
Not here. But in my notebook :S
\[\int\limits_{}^{}\frac{ x }{ x^2+1 }dx = \frac{1}{2}\ln |x^2+1| +C\]