(∫_(-1)^1)(x LegendreP[1,0,x] LegendreP[2,0,x])\[DifferentialD]x

(∫_(-1)^1)(x LegendreP[1,0,x] LegendreP[3,0,x])\[DifferentialD]x

(∫_(-1)^1)(x LegendreP[1,0,x] LegendreP[1,0,x])\[DifferentialD]x

∫(x LegendreP[j,m,x] LegendreP[j2,m,x])\[DifferentialD]x

HermiteH[10,x]

(∫_(-∞)^∞)(HermiteH[1,x] x  HermiteH[0,x]  Exp[-x^2])\[DifferentialD]x

(∫_(-∞)^∞)(HermiteH[1,x] x  HermiteH[1,x]  Exp[-x^2])\[DifferentialD]x

(∫_(-∞)^∞)(HermiteH[2,x] x  HermiteH[0,x]  Exp[-x^2])\[DifferentialD]x

Pi

SphericalHarmonicY[3,1,θ,ϕ]

(∫_0^(2 Pi))((∫_0^Pi)(Conjugate[SphericalHarmonicY[0,0,θ,ϕ]]  SphericalHarmonicY[1,0,θ,ϕ]  Cos[θ])\[DifferentialD]θ)\[DifferentialD]ϕ

(∫_0^(2 Pi))((∫_0^Pi)(Conjugate[SphericalHarmonicY[1,0,θ,ϕ]]  SphericalHarmonicY[1,0,θ,ϕ]  Cos[θ])\[DifferentialD]θ)\[DifferentialD]ϕ

(∫_0^(2 Pi))((∫_0^Pi)(Conjugate[SphericalHarmonicY[2,0,θ,ϕ]]  SphericalHarmonicY[1,0,θ,ϕ]  Cos[θ])\[DifferentialD]θ)\[DifferentialD]ϕ

(∫_0^(2 Pi))((∫_0^Pi)(Conjugate[SphericalHarmonicY[0,0,θ,ϕ]]  SphericalHarmonicY[2,0,θ,ϕ]  Cos[θ])\[DifferentialD]θ)\[DifferentialD]ϕ