Formule de integrare - Sinteze - Matematica M1

Tabel cu integrale nedefinite

Asteptati un moment. Formulele se incarca...

$$ \int a\mathrm{d}x = ax + C$$ $$ \int x^a\mathrm{d}x = {x^{a+1}\over{a+1}} + C$$ $$ \int {1\over x}\mathrm{d}x = \mathrm{ln}|x| + C$$ $$ \int a^{x}\mathrm{d}x = {a^{x}\over \mathrm{ln}a} + C$$ $$ \int e^{x}\mathrm{d}x = e^{x} + C$$ $$ \int {1\over x^2-a^2}\mathrm{d}x = {1\over 2a}\mathrm{ln}\Bigg|{x-a\over x+a}\Bigg| + C$$ $$ \int {1\over x^2+a^2}\mathrm{d}x = {1\over a}\arctan{x\over a} + C$$ $$ \int {1\over \sqrt{a^2-x^2}}\mathrm{d}x = \arcsin{x\over a} + C$$ $$ \int {1\over \sqrt{x^2+a^2}}\mathrm{d}x = \mathrm{ln}(x+\sqrt{x^2+a^2}) + C$$

$$ \int {1\over \sqrt{x^2-a^2}}\mathrm{d}x = \mathrm{ln}\Big|x+\sqrt{x^2-a^2}\Big| + C$$ $$ \int \sin x\mathrm{d}x = -\cos x + C$$ $$ \int \cos x\mathrm{d}x = \sin x + C$$ $$ \int {1\over \cos^2 x}\mathrm{d}x = \tan x + C$$ $$ \int {1\over \sin^2 x}\mathrm{d}x = -\cot x + C$$ $$ \int \tan x\mathrm{d}x = -\mathrm{ln}|\cos x| + C$$ $$ \int \cot x\mathrm{d}x = \mathrm{ln}|\sin x| + C$$ $$ \int \alpha * f(x)\mathrm{d}x = \alpha*\int f(x)\mathrm{dx}$$ $$ \int \big[f(x)\pm g(x)\big]\mathrm{d}x = \int f(x)\mathrm{d}x \pm \int g(x)\mathrm{d}x$$