<s>[INST] Integral of $\int \frac{5x+1}{(2x+1)(x-1)}$ I am suppose to use partial fractions
$$\int \frac{5x+1}{(2x+1)(x-1)}$$
So I think I am suppose to split the top and the bottom. (x-1)
$$\int \frac{A}{(2x+1)}+ \frac{B}{x-1}$$ 
Now I am not sure what to do.
 [/INST] Suppose $\frac{5x+1}{(2x+1)(x-1)} = \frac{A}{2x+1} + \frac{B}{x-1}$. Then $5x+1 = A(x-1)+B(2x+1) = (A+2B)x + (B-A)$. So by comparing coefficients, we get $A+2B = 5$ and $B-A = 1$. Solving this gives $A = 1$ and $B = 2$.
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