Question

Stuck on this integration using 'u' substitution..

integrate (e^x)/(sqrt(4+e^2x))

Answer 1

substitute e^x=t

Answer 2

e^2x is also (e^x)^2?

Answer 3

\[\int\limits_{}^{}e ^{x}dx/\sqrt{4+(e ^{x})^{2}}\]
put e^x=t
derivate both sides wrt to x
(e^x) dx=dt
\[\int\limits_{}^{}dt/\sqrt{(2)^{2}+t ^{2}}\]

Answer 4

now use the formula :
\[\int\limits_{}^{}dt/\sqrt{a ^{2}+t ^{2}}=(1/a)\log \left| (a+t)/(a-t) \right|\]

Answer 5

in final answer dont forget to put t=e^x back

Answer 6

Got it, thanks. It was e^2x throwing me off, forgot you could use (e^x)^2...thanks again

Answer 7

ur welcome