- #1
ArcanaNoir
- 779
- 4
Homework Statement
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]
Homework Equations
[tex] 1+\tan ^2 \theta =\sec ^2 \theta [/tex]
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] ?