Originally Posted by
Soroban Hello, ^_^Engineer_Adam^_^!
I don't agree with the book either . . .
. . . . . . . . . . . .1 . . . . dx
We have: .∫ -------------·---
. . . . . . . . .1 + (ln x)² . x
. . . . . . . . . - . . . . . . dx
Let u = ln x . → . du = ---
. . . . . . . . . . . - . - . . .x
. . . . . . . . . . . du
Substitute: .∫ -------- . = . arctan(u)
. . . . . . . . . . 1 + u²
. . . . - . . . . - . . . - . . . . . . .|e
Back-substitute: .arctan(ln x) |
. . . . - . . . . - . . . - . . . . . . .|1
Evaluate: . arctan(ln e) - arctan(ln 1)
. . . . . .= . arctan(1) - arctan(0)
. . . . . .= . ¼π - 0 . = . ¼π
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
It appears that the author didn't back-substitute.