Integrals
(∫_0^+*∞)(e(-x))*d(x)=(∣_0^+*∞)(-e(-x))=(∣_0^+*∞)(-1/(ex))=1
(∫_0^+*∞)(e(-a*x))*d(x)=1/a,a>0
(∫_0^+*∞)(e(-x2))*d(x)=√(,π)/2,(∫_0^+*∞)(e(-a*x2))*d(x)=1/2√(,π/a)
(∬_R2^)(e(-x2-y2))*d(x) d(y)=π
(∬_R2^)(e(-a*x2-c*y2))*d(x) d(y)=π/√(,a*c),a,c<0
(∬_R2^)(e(-x2-2*ρ*x*y-y2))*d(x) d(y)=π/√(,1-ρ2),abs(ρ)≤1
(∬_R2^)(e(-a*x2-b*x*y-c*y2))*d(x) d(y)=π/√(,a*c-b2),a,c>0
(∫_0^1)((∫_0^1)(1/(1-x*y)))*d(x) d(y)=(π2)/6,(∬_(0,0)^(1,1))(1/(1-x*y)) d(x) d(y)=(π2)/6=ζ(2)
(∬_(0,0)^(1,1))(1/(1+x2*y2)) d(x) d(y)=(∑_n=0^+*∞)(((-1)n)/((2*n+1)2))=𝐺
(∬_(0,0)^(1,1))(1/(1-x2*y2)) d(x) d(y)=(∑_n=0^+*∞)(1/((2*n+1)2))=(π2)/8
(∬_(0,0)^(+∞,+∞))((e(-a*x-b*y))/(c*x+d*y))*d(x) d(y)=(ln(a*d)-ln(b*c))/(a*d-b*c)
(∬_(0,0)^(+∞,+∞))((e(-x-y))/(c*x+d*y))*d(x) d(y)=(ln(d)-ln(c))/(d-c)
(∬_(0,0)^(+∞,+∞))((e(-a*x-b*y))/(x+y))*d(x) d(y)=(ln(a)-ln(b))/(a-b)
(∬_(-∞,-∞)^(+∞,+∞))((x(m-1)*y(n-1)*e(-x-y))/(x+y))*d(x) d(y)=(Γ(m)*Γ(n))/(m+n-1),m+n>1
(∬_(-∞,-∞)^(+∞,+∞))(1/((x2+y2+a2)p))*d(x) d(y)=π/((p-1)*a(2*(p-1))),p>1
(∬_(-∞,-∞)^(+∞,+∞))(1/((x2+y2+a2)2))*d(x) d(y)=π/(a2)
(∬_(0,0)^(1,1))|x-y|p*d(x) d(y)=2/((p+1)*(p+2)),p>-1
(∬_(0,0)^(+∞,+∞))(x(a-1)*y(b-1)*e(-x-y))*d(x) d(y)=Γ(a)*Γ(b)