integral???

Question

how do u intergrate tan x ???

is it: ln (sec x) or is it: ln |sec x|

Answer 1

Your absolute value one is correct. Rewrite tan(x) as sin(x)/cos(x). Then let u=cos(x), so that du= -sin(x)dx. Then our integral turns into:
-1/u du,
which is easily integrated as
-ln |u| + c
-ln |cos(x)| + c

EDIT: Note that if we use the properties of logarithms to move the negative to being an exponent, we get ln |sec(x)|.

It's technically correct to use the absolute value bars, although often it's left out for convenience. So your second answer is technically the better one.

Answer 2

its just...

ln (sec x) or -ln(cos x)

you can simply find it in a table of integrals..

Answer 3

You have to actually do working out as there are a number of steps

1. substitute, s=cos(x), so ds=-sin(x)dx

so the integral is

- (int) 1/s ds

2. The integral of 1/s is = log(s)

so we have

-(int) log(s) + x

Sub back in the value for s

= -(int)log(cos(x)) + c

Answer 4

i think it's just sec x....

Answer 5

God, getting my score up is hard work.