Integrate3
Integrate3
contains the integral table used by Integrate2
. Integration is performed in a distributional sense. Integrate3
works more effectively on a sum of expressions if they are expanded or collected with respect to the integration variable. See the examples in Integrate2
.
See also
Overview, Integrate2.
Examples
Integrate3[x^OPEm Log[x], {x, 0, 1}]
−(m+1)21
Integrate3[(x^OPEm Log[x] Log[1 - x])/(1 - x), {x, 0, 1}]
ζ(2)S1(m)−S12(m)−S21(m)+ζ(3)
Integrate3[a (x^OPEm Log[x] Log[1 - x])/(1 - x) + b (x^OPEm PolyLog[3, -x])/(1 + x), {x, 0, 1}]
a(ζ(2)S1(m)−S12(m)−S21(m)+ζ(3))+b(−1)m(8ζ(2)2+21ζ(2)S−2(m)−43ζ(3)S−1(m)+S3−1(m)+log(2)(S3(m)−S−3(m))−43ζ(3)log(2))
Integrate3[DeltaFunctionPrime[1 - x], {x, 0, 1}]
0
Integrate3[f[x] DeltaFunctionPrime[1 - x], {x, 0, 1}]
f′(1)
Integrate3[1/(1 - x), {x, 0, 1}]
0