Question

Integrate 2/(root 4 - e^(2t) )

Answer 1

i think you use the sub:
e^t = 2sin(theta)

but im verifying that it works

Answer 2

or e^t=u ?

Answer 3

ok it will work

yes that sub will work too but eventually you have to use a trig substitution

Answer 4

should we take s=4-u^2 ?

Answer 5

no...

Answer 6

wait
u = e^t
du = e^t dt
\[\rightarrow \int\limits_{?}^{?} \frac{2}{u \sqrt{4-u^{2}}} du\]

Answer 7

ok..makes sense

Answer 8

then
\[u = 2\sin \theta\]
\[du = 2 \cos \theta d \theta \]
\[\rightarrow \int\limits_{}^{}\frac{2}{(2\sin \theta)\sqrt{4-4\sin^{2} \theta}} (2\cos \theta) d \theta\]
simplify

Answer 9

1/sin theta !

Answer 10

yep

Answer 11

which means, we integrate sin^-1 theta....damn

Answer 12

this will help

http://math2.org/math/integrals/more/csc.htm