| Author |
Comment/Response |
ray
|
 04/30/10 03:02am
tried to integrate the below functions, the answer were trig functions, couldn't get mathematica to generate a trig answer nor would Evaluate equate mathematica's answer to the trig answer. Any idea how I can do this???
Clear["`*"];f[x_]=D[x]/(4+x^2);f1[x_]=(E^x D[x])/Sqrt[1-E^(2x)];f2[x_]=(x D[x])/(x^2 Sqrt[x^4-1]);
Integrate[{f[x],f1[x]},x]
Integrate[f2[x],{x,1,Sqrt[2]}]
what mathematica gave me:
Integrate f[x] = 1/2 Log[4+x^2],
Integrate f1[x] = -(1/2) I (ArcSin[E^x]^2-2 I ArcSin[E^x] Log[1-E^(-2 I ArcSin[E^x])]+2 x Log[I E^x+Sqrt[1-E^(2 x)]]+PolyLog[2,E^(-2 I ArcSin[E^x])])
Integrate f2[x] = (Sqrt[\[Pi]] Gamma[5/4])/Gamma[3/4]-Hypergeometric2F1[1/4,1/2,5/4,1/4]/Sqrt[2]
The answers I was looking for:
f[x] = 1/2 ArcTan[x/2]
f1[x] = ArcSin[E^x]
f2[x] = \[Pi]/6
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