- #1

Potatochip911

- 318

- 3

## Homework Statement

Find the integral of (x-1)/(x^2-4x+5)

## Homework Equations

3. The Attempt at a Solution [/B]

After completing the square I get

∫(x-1)/((x-2)^2+1)*dx

Using substitutions x-2=tanθ; x-1=tanθ+1; dx=sec^2θ*dθ

∫[(tanθ+1)*(sec^2θ*dθ)]/(tan^2θ+1)

After cancelling

∫(tanθ+1)*dθ

integrating this I get

-ln(cosθ)+θ+C

ln(secθ)+θ+C

After substituting x back in

ln(x^2-4x+5)+arctan(x-2)+C

My answer key has a 1/2 infront of the natural log and I'm at a loss as to how they get it.