Here is a list of some formulas for complex integrals that may be useful:

  1. Integral by parts:
    [
    \int u \, dv = uv – \int v \, du
    ]
  2. Substitution integral:
    If ( x = g(t) ), then
    [
    \int f(x) \, dx = \int f(g(t)) g'(t) \,
    dt
  3. Integral from a fraction:
    [
    \int \frac{1}{x^n} \, dx = \frac{x^{-n+1}}{-n+1} + C, \quad n \neq 1
    ]
  4. Integral of trigonometric functions:
    [
    \int \sin(ax) \, dx = -\frac{1}{a} \cos(ax) + C
    ]
    [
    \int \cos(ax) \, dx = \frac{1}{a} \sin(ax) + C
    ]
  5. The exponent integral is:
    [
    \int e^{ax} \, dx = \frac{1}{a} e^{ax} +
    C
  6. Integral of the product of functions (substitution method):
    [
    \int f(g(x)) g'(x) \, dx = F(g(x)) + C
    ]
  7. Integral of the root:
    [
    \int \sqrt{x} \, dx = \frac{2}{3} x^{3/2} + C
    ]
  8. Integral of a fractional rational function (method of decomposition into simplest forms):
    [
    \int \frac{P(x)}{Q(x)} \, dx
    ]
    where ( P(x) ) and ( Q(x) ) are polynomials, and decomposition into simplest forms can be used.

От Math

Добавить комментарий

Ваш адрес email не будет опубликован. Обязательные поля помечены *