Question

help integrating a natural log

Answer 1

Do you know this integral? \(\large\rm \int \sec x~dx\)

Answer 2

If you're more comfortable with a simple inner function like that,
you can do a u-sub to start this off,
\(\Large\rm u=2\pi x+14\)

Answer 3

ah we meet again :DDD

Answer 4

yeah sec(x) is (sec(X)+tan(X)

Answer 5

:D

Answer 6

log of secx + tanx
I think you meant, yes?

Answer 7

pellet mybad

Answer 8

yes

Answer 9

then you sub in u to the x

Answer 10

So if you make a u-sub, you should be able to get it into the form \(\large\rm (number)\int \sec u~ du\) and then you can burn through it pretty fast :)

Answer 11

thnx mane

Answer 12

i subbed it in and got ln(sec(2pix+14)+tan(2pix+14))

it didn't work :/

Answer 13

Very close.
You forgot about your \(\Large\rm du\)

Answer 14

\[\Large\rm u=2\pi x+14, \qquad\qquad du=?\]

Answer 15

2pi

Answer 16

You can't integrate \(\Large\rm \int \sec u ~dx\)
Gotta deal with the differential also.\[\Large\rm du=2\pi dx\]Ok great, so what are we subbing in for dx?
Solve for your dx in this relationship.

Answer 17

du/2pi=dx

or do i need

x(u)=c+u/2pi

Answer 18

Mmm k that looks great,\[\Large\rm \frac{1}{2\pi}du=dx\]

Answer 19

log(abs(sec(2pix+14)+tan(2pix+14)))/(2pi)

Answer 20

got it, thanks again!

Answer 21

yay!