Hi, I am trying to integrate some functions in Wolfram Alpha Pro, but the result I get uses a hyperbolic function, but since we have not learned that still at university, is it possible that I receive as a result a nonhyperbolic function?
eg. integrate e^x/(4+e^(2x))^1/2
the result: sinh^(-1)(e^x/2)
Thanks in advance.
Integrate[e^x/(4 + e^(2 x))^1/2, x]
% // TrigToExp
-(ArcTan[2 e^-x]/(4 Log[e]))
-((I Log[1 - 2 I e^-x])/(8 Log[e])) + (I Log[1 + 2 I e^-x])/(8 Log[e])
Hi @Jose, thanks for the reply! The thing is I am using Wolfram Alpha and not Mathematica!
If you look below the sinh^-1 result you will see WolframAlpha also provides an alternate form of the result as a log
The alternate form is
log(sqrt(e^(2 x)/4 + 1) + e^x/2) + constant