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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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