Primitives
Primitives usuelles
Primitives usuelles
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Lernkarten
\(a\)
\(ax\)
\(x^n\)
\(\frac{x^{n+1}}{n+1}\)
\(\frac{1}{x}\)
\(\ln x\)
\(\frac{1}{x^n}\)
\(\frac{-1}{(n-1)x^{n-1}}\)
\(\sqrt{x}\)
\(\frac23x\sqrt x\)
\(\frac 1 {\sqrt{x}}\)
\(2\sqrt x\)
\(\frac{1}{(x-a)(x-b)}\)
\(\frac{1}{a-b}\ln(\frac{x-a}{x-b})\)
\(\frac{ax+b}{cx+d}\)
\(\frac{ax}{c}-\frac{ab-bc}{c^2}\ln(cx+d)\)
\(\frac 1{x^2+a^2}\)
\(\frac1a \arctan(\frac{x}{a})\)
\(\frac1{x^2-a^2}\)
\(\frac{1}{2a}\ln(\frac{x-a}{x+a})\)
\(e^x\)
\(e^x\)
\(\ln x\)
\(x(\ln x -1)\)
\(a^x\)
\(\frac{a^x}{\ln a}\)
\(xe^{ax}\)
\(\frac{1}{a^2}(ax-1)e^{ax}\)
\(x\ln ax\)
\(\frac{x^2}{4}(2\ln ax-1)\)
\(\sin x\)
\(-\cos x\)
\(\cos x\)
\(\sin x\)
\(\tan x\)
\(-\ln(\cos x) // 1+\tan^2x\)
\(\cot x\)
\(\ln(\sin x)\)
\(\arcsin x\)
\(x\arcsin x+\sqrt{1-x^2}\)
\(\arccos x\)
\(-\frac{1}{\sqrt{1-x^2}}\)
\(\arctan x\)
\(\frac{1}{x^2+1}\)
\(\frac{x^2}{1+x^2}\)
\(x-\arctan x\)
\(\frac{1}{1-x^2}\)
\(\tanh^{-1}x\)
\(\frac{1}{\sqrt{a^2-x^2}}\)
\(\arcsin(\frac{x}{a})\)
