Question

integrate: ( 1/sqr(1-(e^(-x)))) dx, substitute: e^(-x)=u^2

Answer 1

ok after substituting you get
\[-e^{-x} dx = 2u du\]
\[dx = -\frac{2u du}{e^{-x}} = -\frac{2u du}{u^{2}} = -\frac{2 du}{u}\]
\[\rightarrow -2 \int\limits \frac{du}{u \sqrt{1-u^{2}}}\]
now let u = cos(theta)
\[du = -\sin \theta d \theta\]
\[\rightarrow 2 \int\limits \sec \theta d \theta = 2 \ln (\sec \theta +\tan\theta)\]

Answer 2

what is u =sin(theta) .. why did you choose cos(theta)?

Answer 3

*what if u is sin(theta)..?

Answer 4

@hpfan5 sorry i left without logging off by accident
anyway, you are right you could sub either sin or cos for u and it would still work
i chose "u = cos" because integral of sec is easier than integral of csc

Answer 5

ok thank you :)