Unbestimmte Integrale

(Siehe Bronstein, Taschenbuch der Mathematik [BSMM00, pp. 445])

Funktion	Integral
$x^n$	$\int x^n dx = \frac{x^{n+1}}{n+1}$	$n\neq -1$
$\frac{1}{x}$	$\int \frac {dx}{x} = \ln\vert x\vert$
$\sin(x)$	$\int \sin (x) dx =-\cos(x)$
$\cos(x)$	$\int \cos (x) dx = \sin(x)$
$\tan(x)$	$\int \tan (x) dx =-\ln\vert\cos(x)\vert$
$\cot(x)$	$\int \cot (x) dx = \ln\vert\sin(x)\vert$
$\frac{1}{\cos^2(x)}$	$\int \frac{dx}{\cos^2(x)} = \tan(x)$
$\frac{1}{\sin^2(x)}$	$\int \frac{dx}{\sin^2(x)} = -\cot(x)$
$\frac{1}{a^2+x^2}$	$\int \frac{dx}{a^2+x^2} = \frac{1}{a}\arctan\frac{x}{a}$
$e^x$	$\int e^x dx = e^x$
$a^x$	$\int a^x dx = \frac{a^x}{\ln a}$
$\ln x$	$\int \ln x dx = x \ln x -x$

Unbestimmte Integrale I

Funktion	Integral
$\sinh x$	$\int \sinh x dx = \cosh x$
$\cosh x$	$\int \cosh x dx = \sinh x$
$\tanh x$	$\int \tanh x dx = \ln\vert\cosh x\vert$
$\coth x$	$\int \coth x dx = \ln\vert\sinh x\vert$
$\frac{1}{\cosh^2 x}$	$\int \frac{dx}{\cosh^2 x} = \tanh x$
$\frac{1}{\sinh^2 x}$	$\int \frac{dx}{\sinh^2 x} = -\coth x$
$\frac{1}{\sqrt{a^2-x^2}}$	$\int\frac{dx}{\sqrt{a^2-x^2}}=\arcsin\frac{x}{a}$

Unbestimmte Integrale II