I'm stuck on intergrating a function. the function is (x-2)/(x^2-4x+5)^.5. The problem states that we are to use (x-2)^2 as u for subsition. So i took the derivative of (x-2)^2 and plugged du into the intergal. Then I'm stuck. I have .5*the intergal of du/(u+1)^.5. I don't know what to do after that. Any help?
Hello, flash!
They surely suggested that substitution to give you practice,
. . but there is a simpler way . . .
. . . . . . . . . . .(x - 2) dx
We have: . ∫ --------------- . = . ∫ (x² - 4x + 5)^{-½} (x - 2) dx
. . . . . . . . . √x² - 4x + 5
Let: .u .= .x² - 4x + 5 . . → . . du .= .(2x - 4)dx . . → . . dx .= .du/2(x-2)
Substitute and we have: .½ ∫ u^{-½} du