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## Main Question or Discussion Point

When you have to integrate a function that requires substitution and you integrate it again, why is it wrong to keep the initial substitution?

e.g. y''=2x/(1+x^2)^2

If you let u=1+x^2 then y'=-(1/u)+C. Why is it wrong to integrate that again with respect to u and then change back to x at the end? I know it's not right but I can't see why

e.g. y''=2x/(1+x^2)^2

If you let u=1+x^2 then y'=-(1/u)+C. Why is it wrong to integrate that again with respect to u and then change back to x at the end? I know it's not right but I can't see why