- #1

MillerGenuine

- 64

- 0

## Homework Statement

[tex] \int arctan(4t) [/tex]

## Homework Equations

I know what the answer is to the problem but when i look at the solution i have no idea how they get from one step to the next.

## The Attempt at a Solution

once we integrate by parts we get

[tex] 1/4 U arctan(U) - 1/4 \int U/1+U^2 [/tex] where U= 4t

from this they go to..

[tex] 1/4 U arctan(U) - 1/8 \int 2U/1+U^2 [/tex]

clearly a 2 was multiplied inside and a 1/2 on the outside of the integral, but why? and how? because the next step shown is..

[tex] 1/4 (4t arctan(4t) - 1/8 ln 16t^2 + c [/tex]

which is the answer..i get that 4t was substituted back in for U, but i don't understand how and why the 2 was put in the integral and the 1/2 outside of it, and how in the last step the 2U somehow is gone?