Question

integrate sqrt(1+e^(2x))..help please

Answer 1

did you try the u sub
\(\Large u= e^x\)
?

Answer 2

a trig sub will be better
\(\Large e^x = \tan u\)

Answer 3

i will try it

Answer 4

what will be dx = ....?
in terms of 'u' only?

Answer 5

Alternatively if you like partial fractions, try \(\sqrt{1+e^{2x}} = u \)
it gives a nice fraction to integrate :)

Answer 6

please try this substitution:
\[\sqrt{1+e ^{2x}}=e ^{x}+t\]
where t is your new variable of integration.
Please square both sides and try to solve for e^x
you should get this:
\[e ^{x}=\frac{ 1-t ^{2} }{ 2t }\]

Answer 7

Awesome!
so many different ways to integrate the same function :D