Solving the integral $\int \frac{2dx}{(x-2)(x-1)x}$

Question

$\int \frac{2dx}{(x-2)(x-1)x}$

Any help with how to solve this will be appreciated.

What method do you think will apply? You must have worked with this type of expression before. How do you "simplify" such an expression for the purpose of integrating it? — John Wayland Bales, Feb 04 '17 at 03:35
Converting the expression into a sum! Pretty easy, it just didn't click before. — user405925, Feb 04 '17 at 03:41
Typically, you will get more help and more upvotes if you indicate what you've tried, and show where you get stuck. — The Count, Feb 04 '17 at 03:54

Momo · Accepted Answer · 2017-02-04T03:39:59.810

2

Partial fraction expansion

$$\frac{2}{(x-2)(x-1)x}=\frac{1}{x}-\frac{2}{x-1}+\frac{1}{x-2}$$

The rest is easy.

edited Feb 04 '17 at 03:39

answered Feb 04 '17 at 03:34

Momo

2

Thankyou! It will take some time for the right approach to click right away i guess. – user405925 Feb 04 '17 at 03:42

1 Answers1