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Indefinite integral in division form

Elina_Gilbert

New member
Sep 3, 2021
1
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
Jan 26, 2012
1,460
May I ask what context this integral comes from?