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evaluate the integral of e^x/2 between ln9 and ln4? 

 May 2, 2020
 #1
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    Take the integral:

\[Integral]E^Sqrt[r]/Sqrt[r] \[DifferentialD]r

 

 

For the integrand E^Sqrt[r]/Sqrt[r], substitute u==Sqrt[r] and \[DifferentialD]u==1/(2 Sqrt[r])\[ThinSpace]\[DifferentialD]r:

 == 2\[Integral]E^u \[DifferentialD]u

 

 

The integral of E^u is E^u:

 == 2 E^u+constant

 

 

Substitute back for u==Sqrt[r]:

Answer: \[SpanFromLeft]

== 2 E^Sqrt[r]+constant   - Courtesy of Mathematica 11 Home Edition

 May 2, 2020

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