## Online Course Discussion Forum

### Calculus BC- antideriv of functions with multiplicative terms

Calculus BC- antideriv of functions with multiplicative terms

Hello,

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

For this type of questions you can try substitution method: Let $u=x^2+1$, and then $du=2xdx$, and go from there.