TrickIntegrate
TrickIntegrate[(1 - t)^(a * Epsilon - 1) g[t], t]
does an integration trick for the definite integral of ((1−t)aEpsilon−1 g[t]) from 0
to 1
, yielding g[1]/a/Epsilon + Hold[Integrate][(1-t)^{a Epsilon-1} (g[t]-g[1]),{t,0,1}]
TrickIntegrate[t^(a Epsilon-1) g[t], t]
gives aEpsilong[0]+ Hold[Integrate][taEpsilon−1 (g[t]-g[0]),{t,0,1}], provided g[1] and g[0] exist.
See also
Overview, Epsilon.
Examples
TrickIntegrate[(1 - t)^(a Epsilon - 1) g[t], t]
Hold[Integrate][g(t)(1−t)aε−1,{t,0,1}]
TrickIntegrate[t^(a Epsilon - 1) g[t], t]
Hold[Integrate][g(t)taε−1,{t,0,1}]