FANDOM


Standard functionsEdit

  • \int a dx = ax + C
  • \int x^n dx = \frac{x^{n+1}}{n+1} + C,n \ne -1
  • \int f(x)g(x) dx = f(x) \int g(x) dx - \int f'(x) (\int g(x) dx) dx (integration by parts)

Logarithmic and exponential functionsEdit

  • \int a^x dx = \frac{a^x}{\ln(a)} + C
  • \int e^x dx = e^x + C
  • \int \frac{dx}{x} = \ln|x| + C
  • \int \ln(x) dx = x \ln (x) - x + C
  •  \int \log_a (x)dx = x\log_a x - \frac{a^x}{\ln(a)} + C

Trigonometric functionsEdit

  • \int \sin(x) dx = -\cos (x) + C
  • \int \cos(x) dx = \sin (x) + C
  • \int \tan(x) dx = -\ln | \cos(x) | + C = \ln |\sec(x)| + C
  • \int \csc(x) dx = \ln|\tan (\frac{x}{2})| + C
  • \int \sec(x) dx = \ln|\sec(x) + \tan (x)| + C
  • \int \cot(x) dx = \ln|\sin(x)| + C
  • \int \frac{dx}{\sqrt{1-x^2}} = \arcsin(x) + C
  • \int -\frac{dx}{\sqrt{1-x^2}} = \arccos(x) + C
  • \int \frac{dx}{1+x^2} = \arctan(x) + C
  • \int -\frac{dx}{1+x^2} = \arccot(x) + C
  • \int \frac{dx}{x \sqrt{x^2-1}} = \arcsec|x| + C
  • \int -\frac{dx}{x \sqrt{x^2-1}} = \arccsc|x| + C

See alsoEdit

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.