Matemaatika:Määramata integraal

$\int x\mathrm{d}x=x+C$

$\int x^{\alpha }\mathrm{d}x=\frac{x^{\alpha }+1}{\alpha +1}+C$(α ≠ -1)

$\int \frac{1}{x}\mathrm{d}x=ln|x|+C$

$\int x^e\mathrm{d}x=e+C$

$\int a^x\mathrm{d}x=\frac{a^x}{ln(a)}+C$

$\int sin(x)\mathrm{d}x=-cos(x)+C$

$\int cos(x)\mathrm{d}x=sin(x)+C$

$\int \frac{1}{co{s}^2(x)}\mathrm{d}x=tan(x)+C$

$\int \frac{1}{si{n}^2(x)}\mathrm{d}x=-cot(x)+C$

$\int \frac{1}{\sqrt{1-x^2}}\mathrm{d}x=arcsin(x)+C=-arccos(x)+C$

$\int \frac{1}{1-x^2}\mathrm{d}x=arctan(x)+C$

$\int \frac{1}{x^2}\mathrm{d}x=-\frac{1}{x}+C$

$\int \frac{1}{2\sqrt{x}}\mathrm{d}x=\sqrt{x}+C$

$\int a\ast f(x)\mathrm{d}x=a\int f(x)\mathrm{d}x$

$\int [f(x)+g(x)]\mathrm{d}x=\int f(x)\mathrm{d}x+\int g(x)\mathrm{d}x$

$\int f(a\ast x+b)\mathrm{d}x=\frac{1}{a}\ast f(a\ast x+b)+C$

$\int \mathrm{d}(cos(x))=cos(x)+C$

$\int \frac{u+v}{x}\mathrm{d}x=\int \frac{u}{x}\mathrm{d}x+\int \frac{v}{x}\mathrm{d}x$