<math>\begin{align} & I=\int_{a^b}f(x)dx=\int_{a^{x4} }f(x)dx=\int_{a^{a+4b} }f(x)dx,gdziex_i=a+ihorazh=\frac{(b-a)}{4} \\ & I=\int_{a^{a+4h} }f(x)dx=h[4f(a)+8\Delta f(a)+( \frac{64}{3}-8)\frac{\Delta^2f(x_0)}{2!}+(64-64+16)\frac{\Delta^3f(x_0)}{3!}+ (\frac{1024}{5}-384+\frac{704}{3}-48)\frac{\Delta^4 f(x_0)}{4!}] \\ & I=[4f(a)+8(f(a+h)-f(a))+\frac{20}{3}(f(a+2h)-2f(a+h)+f(a))+\frac{8}{3}(f(a+3h)-3f(a+2h)+3f(a+h)-f(a))+\frac{14}{45}(f(a+4h)-4f(a+3h)+6f(a+2h)-4f(a+h)+f(a))] \\ & I=\frac{h}{45}[14f(a)+64f(a+h)+24f(a+2h)+64f(a+3h)+14f(a+4h)] \\ & I=\frac{2h}{45}[7f(a)+32f(a+h)+12f(a+2h)+32f(a+3h)+7f(a+4h)] \\ & I=\frac{2h}{45}(7f(a)+32f(x_1)+12f(x_2)+32f(x_3)+7f(b)) \end{align}</math>

${\displaystyle {\begin{aligned}&I=\int _{a^{b}}f(x)dx=\int _{a^{x4}}f(x)dx=\int _{a^{a+4b}}f(x)dx,gdziex_{i}=a+ihorazh={\frac {(b-a)}{4}}\\&I=\int _{a^{a+4h}}f(x)dx=h[4f(a)+8\Delta f(a)+({\frac {64}{3}}-8){\frac {\Delta ^{2}f(x_{0})}{2!}}+(64-64+16){\frac {\Delta ^{3}f(x_{0})}{3!}}+({\frac {1024}{5}}-384+{\frac {704}{3}}-48){\frac {\Delta ^{4}f(x_{0})}{4!}}]\\&I=[4f(a)+8(f(a+h)-f(a))+{\frac {20}{3}}(f(a+2h)-2f(a+h)+f(a))+{\frac {8}{3}}(f(a+3h)-3f(a+2h)+3f(a+h)-f(a))+{\frac {14}{45}}(f(a+4h)-4f(a+3h)+6f(a+2h)-4f(a+h)+f(a))]\\&I={\frac {h}{45}}[14f(a)+64f(a+h)+24f(a+2h)+64f(a+3h)+14f(a+4h)]\\&I={\frac {2h}{45}}[7f(a)+32f(a+h)+12f(a+2h)+32f(a+3h)+7f(a+4h)]\\&I={\frac {2h}{45}}(7f(a)+32f(x_{1})+12f(x_{2})+32f(x_{3})+7f(b))\end{aligned}}}$

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