I am working on a problem at the moment which i have the answer for but i don't understand one step of the solution.
Evaluate "integration sign" (2x-6)dx/[(x^2)-6x+10]
The answer is given as Ln2.
I can see how the answer comes about but a step of it is confusing me.
Once i substitue and solve i get Ln[1x^2)-6(x)+10]/??? as per the rule for integrating 1/ax+b=ln(ax+b)/a
In otherwords 1/ax+b=(1[ln(ax+b)]/a) +c
However which value do i pic for a? It seems there are 2 coefficients of x in this case, 1 for the x squared, and -6 for the x.
It looks like the a chosen in the solution is the coefficient of the X^2 which is 1.
Why is the coefficient of the -6x not used for the a ?
It seems a pretty fundemental issue that i need solved.
When given a quadratic expression & when integrating is the a coefficient for the solution always the coefficient associated with the x^2?
Apologies if this is a ridiculous question