# Thread: Integration Problem - # 2

1. ## Integration Problem - # 2

$\displaystyle \int \dfrac{\sec x }{\sqrt{\ln(\sec x + \tan x)}} dx$

hint?

I do know the integral of $\displaystyle \sec x + \tan x$ is $\displaystyle \sec x$, but the $\displaystyle \ln$ thing is causing a problem, as well as the square root.

2. ## Re: Integration Problem - # 2

$\displaystyle u = \ln(\sec{x} + \tan{x})$

$\displaystyle du = \sec{x} \, dx$

substitute ...

3. ## Re: Integration Problem - # 2

$\displaystyle \int \dfrac{\sec x }{\sqrt{\ln(\sec x + \tan x)}} dx$

$\displaystyle u = \sec x \tan x$

$\displaystyle du = \sec x dx$

$\displaystyle \int \dfrac{du }{\sqrt{\ln(u)}}$ ??? Next step?

4. ## Re: Integration Problem - # 2

If u= ln(sec(x)+ tan(x)), what is du in terms of dx?

Do you know the derivatives of sec(x) and tan(x)?

5. ## Re: Integration Problem - # 2

Originally Posted by Jason76
$\displaystyle \int \dfrac{\sec x }{\sqrt{\ln(\sec x + \tan x)}} dx$

$\displaystyle u = \sec x \tan x$

$\displaystyle du = \sec x dx$

$\displaystyle \int \dfrac{du }{\sqrt{\ln(u)}}$ ??? Next step?