# Math Help - Integral of sec(6x)tan(6x)

1. ## Integral of sec(6x)tan(6x)

again, it's:

Integral of: sec(6x)tan(6x)

Thanks!

2. Originally Posted by sj9110

again, it's:

Integral of: sec(6x)tan(6x)

Thanks!
Try this substitution $u=6x$.

3. actually i just realized the whole thing is in parentheses if that makes a difference

intsec(6x)tan(6x))dx

4. Originally Posted by sj9110
actually i just realized the whole thing is in parentheses if that makes a difference

intsec(6x)tan(6x))dx
Did you try what I said?

5. yes, but i'm stuck at

(1/6) integral [sec(u)tan(u)]du

6. Originally Posted by sj9110
yes, but i'm stuck at

(1/6) integral [sec(u)tan(u)]du
What is the derivative of $sec(u)$ ?

7. sec(x)tan(x) ...but i don't see how to incorporate it all.

8. If the derivative of $g(x)$ is $f(x),$ it means that the integral of $f(x)$ is $g(x)$ plus a constant.

9. Originally Posted by sj9110
sec(x)tan(x) ...but i don't see how to incorporate it all.
No. Its sec(u)tan(u).

If the derivative of sec(u) is sec(u)tan(u) .. then what is the integral of sec(u)tan(u) ?

Excause me, Do you know the Fundamental Theorem of Calculus ?

10. i got an answer of (1/6)sec(6x) + c ... is this right?

11. Originally Posted by sj9110
i got an answer of (1/6)sec(6x) + c ... is this right?
Yes. You are correct.

12. Originally Posted by General
No. Its sec(u)tan(u).

If the derivative of sec(u) is sec(u)tan(u) .. then what is the integral of sec(u)tan(u) ?

Excause me, Do you know the Fundamental Theorem of Calculus ?
It's been a year since I took calculus 1 and 2, so I am pretty rusty.

13. Originally Posted by General
Yes. You are correct.
great!..i was just getting a bit confused with all the substitution and stuff. Thanks for your help!