чернетка
1 ) I ( y ) = ∫ 1 ∞ cos ( x 2 + y ) x + y d x {\displaystyle 1)\quad I(y)=\int \limits _{1}^{\infty }{\cos(x^{2}+y) \over x+y}dx} δ H δ t = 0 {\displaystyle {\delta H \over \delta t}=0}
2 ) I ( α ) = ∫ 0 ∞ sin 2 x sin α x x 3 d x {\displaystyle 2)\quad I(\alpha )=\int \limits _{0}^{\infty }{\sin ^{2}x\sin \alpha x \over x^{3}}dx}
3 ) f ( x ) = 1 a 2 + x 2 ( a ≥ 0 ) {\displaystyle 3)\quad f(x)={1 \over a^{2}+x^{2}}\quad (a\geq 0)}
∫ y ∞ e 3 x sin 2 α x x 5 3 ln | x | d x {\displaystyle \int \limits _{y}^{\infty }{e^{3x}\sin ^{2}\alpha x \over x^{5 \over 3}{\sqrt {\ln |x|}}}dx}
G ( R → , τ ) = c 4 π R δ ( c τ − R ) {\displaystyle G({\vec {R}},\tau )={c \over 4\pi R}\;\delta (c\tau -R)}