Using partial fraction techniques to work out following intergrals Hello I am studying for a mock test that is coming up, a question very similar to this one will be on this test, I have no idea how to complete this type of question, I have been given some vague notes about how I should turn it into a arctan function (??? I have no idea how to)
Here is the question:
$$I=\int\frac{5x^{2}-10x}{(9x^{2}-16)(x^{2}+1)}\:\mathrm{d}x$$
I've 'Simplified' down to: 
$$\frac{5x^2-10x}{(3x-4)(3x-4)(x^2+1)}$$
Here is the stage I have gotten to so far:
$$I = \int\left(\frac{A}{3x-4} + \frac{B}{3x-4} + Cx+\frac{D}{x^2+1}\right)\:\mathrm{d}x$$

See  Partial Fraction Decomposition
$$\dfrac{5x^2-10x}{(9x^2-16)(x^2+1)}=\dfrac A{3x-4}+\dfrac B{3x+4}+\dfrac{Cx+D}{x^2+1}$$
$$\implies5x^2-10x$$
$$=A(3x+4)(x^2+1)+B(3x-4)(x^2+1)+(Cx+D)(3x+4)(3x-4)$$
Set $3x-4=0,3x+4=0$ one by one to find $A,B$
Now compare the coefficients of $x^3,$  $$0=3A+3B+9C\iff C=?$$
compare the constants $$4A-4B-16D=0\iff D=?$$
