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Calculus BC- antideriv of functions with multiplicative terms
I am confused on getting antiderivatives of functions with multiplicative terms (ex. denominators).
Specifically, #11 of 7/18 hw, get the antiderivative of x/(x^2 + 1)? To me this seems like a triple nested function like (f(g(h(x)))). I also cannot apply the trick of NUM/(denom1 * denom2) = A/denom1 + B/denom2 as (x^2 + 1) is non-factorable over the reals. I also can't readily use FOIL to break this derivative function into additive discrete terms because of the denominator.
I am also a bit lost on Euler's method of stepping; I got a different answer than the key
Below please find the problem