Lukion taulukot/Integraalifunktioita

Intergraalifunktioita

$f(x)$	$F(x)=\int f(x)\mathrm{d}x+C$
$k$	$kx+C$
$x^n(n\ne -1)$	$\frac{1}{n+1}{x}^{n+1}+C$
$\frac{1}{x}(x\ne 0)$	$\ln |x|+C$
$e^x$	$e^x+C$
$a^x(a>0,a\ne 1)$	$\frac{1}{\ln a}{a}^x+C$
$\frac{1}{x-a}$	$\ln |x-a|+C$
$\frac{1}{\sqrt{1-x^2}}$	$\arcsin x+C$
$\frac{1}{x^2+a^2}$	$\frac{1}{a}\arctan \frac{x}{a}+C$
$\frac{x}{x^2+a^2}$	$\frac{1}{2}\ln (x^2+a^2)+C$
$\sin x$	$-\cos x+C$
${\sin }^{2}x$	$\frac{1}{2}(x-\sin x\cos x)+C$
$\cos x$	$\sin x+C$
${\cos }^{2}x$	$\frac{1}{2}(x+\sin x\cos x)+C$
$\tan x$	$-\ln |\cos x|+C$
$\cot x$	$\ln |\sin x|+C$
$\frac{1}{{\sin }^{2}x}$	$-\cot x+C$
$\frac{1}{{\cos }^{2}x}$	$\tan x+C$
$f(x{)}^n\cdot f^{\prime }(x)(n\in ℝ,n\ne -1)$	$\frac{1}{n+1}f(x{)}^{n+1}+C$
$\frac{f^{\prime }(x)}{f(x)}$	$\ln |f(x)|+C$
${\mathrm{e}}^{f(x)}{f}^{\prime }(x)$	${\mathrm{e}}^{f(x)}+C$
$\ln |x|(x\ne 0)$	$x\ln |x|-x+C$