# Indefinite integral in division form

#### Elina_Gilbert

##### New member
I have the following integration -

$$\int \frac{2}{x - b \frac{x^{m - n + 1}}{(-x + 1)^m}} \, dx$$

To solve this I did the following -
$$\int \frac{1 - b \frac{x^{m - n}}{(-x + 1)^m}+1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx$$

Which gives me -

$$log(x) + C+ \int \frac{1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx$$

No matter what substitution I do, I couldn't solve the integral -

$$\int \frac{1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx$$

Can anyone please suggest what I did wrong? Please suggest me another method to solve this?

#### Prove It

##### Well-known member
MHB Math Helper
May I ask what context this integral comes from?