How do you find #int 8/ ( x^2 (x+3) )dx# using partial fractions?
Apply partial fractions to find
In partial fraction decomposition, we consider denominators which could combine to create the original denominator as the common denominator, and then solve for the numerators.
As the factors of
Now, multiplying through by
Now, we equate corresponding coefficients to obtain the system
Solving the system, we obtain
Then we substitute back into our original equation to obtain
Now we proceed to integrate.