Thread: Solving undefined integral with new variable

1. Solving undefined integral with new variable

Hy i have a little problem with solving integral. I have to use new variable as $t=Sin(x)$

$\int \! {Cos(x) \over {Sin(x)^2-3 Sin(x)+2}} \, dx$

But i don't know how to start.

2. Originally Posted by PJani
Hy i have a little problem with solving integral. I have to use new variable as $t=Sin(x)$

$\int \! {Cos(x) \over {Sin(x)^2-3 Sin(x)+2}} \, dx$

But i don't know how to start.
To start set $t= \sin{x}$ . Then:

$dt = dx \cos{x}$ and so the integral becomes $\int \frac{dt}{t^2-3t+2}$

To proceed try completing the square in the denominator. This should be enough to get you started. Good luck.

3. There's no need to complete the square, use that $t^2-3t+2=(t-1)(t-2).$