Online Course Discussion Forum

Calculus BC- antideriv of functions with multiplicative terms

 
 
Picture of selina z
Calculus BC- antideriv of functions with multiplicative terms
by selina z - Sunday, August 7, 2022, 11:45 AM
 

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

Below please find the problem

Thank you!

 
Picture of Dr. Kevin Wang
Re: Calculus BC- antideriv of functions with multiplicative terms
by Dr. Kevin Wang - Sunday, August 7, 2022, 3:09 PM
 

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