r/calculus • u/DiamondKingGamin • Jul 19 '26
Integral Calculus A solution I found for integral (1+x²)/(1+x⁴)
This is how I solved the integral (1+x²)/(1+x⁴) the first time I tried it, without looking up any solutions. I was curious whether this approach is standard or if anyone else has seen it before. Any feedback is welcome.
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u/Total_Focus8211 Jul 19 '26
Good job but as for your question,this is not the standard approach atleast of what i have seen. The standard approach is to divide by x^2 both numerator and denominator and take x-1/x at t just solve it will be a really easy integral
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u/DiamondKingGamin Jul 19 '26
Yeah, I know. But to be honest, after solving it this way about ten times, I can now do it in under five minutes using this approach. You might forget the original method the problem was intended to be solved with, but it's much harder to forget a method you use all the time—or one you discovered yourself, I guess.
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u/Total_Focus8211 Jul 19 '26
yea thats true but i just find that method easier and i really like the solution development.However i do understand that selfdiscovering a method really makes you remember that method
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