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[✓] Integrate and get a result without hyperbolic functions?

GROUPS:

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.

POSTED BY: Medina Tochi
Answer
21 days ago
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])

POSTED BY: Jose Calderon
Answer
21 days ago

Hi @Jose, thanks for the reply! The thing is I am using Wolfram Alpha and not Mathematica!

POSTED BY: Medina Tochi
Answer
21 days ago

If you look below the sinh^-1 result you will see WolframAlpha also provides an alternate form of the result as a log

POSTED BY: Bill Simpson
Answer
21 days ago

The alternate form is log(sqrt(e^(2 x)/4 + 1) + e^x/2) + constant

POSTED BY: Jose Calderon
Answer
20 days ago

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