Hi, I'm trying to figure out what's wrong here if anything.
∫(x+2)/(x^2 - 1)
by solving with partial fractions I get integrals: ∫3/(2(x-1)) - ∫1/(2(x+1))
and then the result: (3/2)(ln(x-1)) - (1/2)(ln(x+1)) + C
but solving by first rewriting the problem as: ∫x/(x^2 - 1) + ∫2/(x^2 - 1)
gives the result: (1/2)ln|x^2 - 1| + ln|x-1| - ln|x+1| + C
Please help explain if something is wrong or if the two answers look different but are the same.
∫(x+2)/(x^2 - 1)
by solving with partial fractions I get integrals: ∫3/(2(x-1)) - ∫1/(2(x+1))
and then the result: (3/2)(ln(x-1)) - (1/2)(ln(x+1)) + C
but solving by first rewriting the problem as: ∫x/(x^2 - 1) + ∫2/(x^2 - 1)
gives the result: (1/2)ln|x^2 - 1| + ln|x-1| - ln|x+1| + C
Please help explain if something is wrong or if the two answers look different but are the same.