Question

help me integrate this one please. :)

Answer 1

\[\int\limits_{}^{} \frac{e^{2x}}{\sqrt{1-e ^{2x}) }} dx\]

Answer 2

trigonometric substitution.

Answer 3

let e^x = sin(x) for example

Answer 4

sin(alpha) not x. would make less sense.

Answer 5

\[ e^x= sin(\alpha)\] \[ e^x dx = cos(\alpha) d\alpha \]

\[ \large \int \frac{\overbrace{e^x}^{sin\alpha}\overbrace{e^xdx}^{cos\alpha d\alpha}}{\sqrt{1-\underbrace{e^{2x}}}_{sin^2\alpha}} \]

Answer 6

so I get \[ -\sqrt{1-e^{-2x}}\] after integrating and back substitution

Answer 7

mention when something is unclear @kaiz122

Answer 8

can we just let \[u=e^{x}\] ?

Answer 9

that should work too but it might require another substitution, that's only how my mind works though. The denominator cries out for trig substitution (in my eyes), but there are various ways of solving it I am sure.

Answer 10

yes, your answer is right, but i just wanted another solution for this. :)

Answer 11

ok, thanks, i got it now. :)

Answer 12

your welcome, I tried it out with an u substitution too, it works, but requires an additional substitution. No problem though, always choose what's the most intuitive to you.