(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I got to a place in a problem where I need to do a sticky integral, and I'm hoping I can use a trig substitution. If not, I will need to solve the main problem another way :(

[tex] \int_0^\infty \sqrt{1+(e^{-\theta })^2} \; \mathrm{d} \theta [/tex]

2. Relevant equations

[tex] 1+\tan ^2 \theta =\sec ^2 \theta [/tex]

3. The attempt at a solution

Can I let [itex] e^{- \theta } = \tan \phi [/itex] ?

if so, does [itex] \mathrm{d} \theta = \sec ^2 \phi \; \mathrm{d} \phi [/itex] ?

And then, do I have

[tex] \int \sec ^3 \phi \; \mathrm{d} \phi [/tex] ?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trig substitution integral (I hope)

**Physics Forums | Science Articles, Homework Help, Discussion**