# Integrali i Pacaktuar. Tabela dhe vetitë

F(x) quhet primitive e funksionit f(x) nese F'(x)=f(x). Bashkesina e primitivave F(x)+c te funksionit f(x) quhet integral i pacaktuar i funksionit f(x).

##### Tabela e integraleve

$1)&space;\int&space;x^{\alpha&space;}dx=\frac{x^{\alpha&space;+1}}{\alpha&space;+1}+c$

$2)\int&space;dx=x+c$

$3)\int&space;\frac{dx}{\sqrt{x}}=2\sqrt{x}+c$

$4)\int&space;\frac{dx}{x}=ln\left&space;|&space;x&space;\right&space;|+c$

$5)\int&space;a^{x}dx=\frac{a^{x}}{lna}+c$

$6)\int&space;e^{x}dx=e^{x}+c$

$7)\int&space;sinxdx=-cosx+c$

$8)\int&space;cosdx=sinx+c$

$9)\int&space;\frac{dx}{cos^{2}x}=tgx+c$

$10)\int&space;\frac{dx}{sin^{2}x}=-cotgx+c$

$11)\int&space;\frac{dx}{x^{2}-a^{2}}=\frac{1}{2a}ln\left&space;|&space;\frac{x-a}{x+a}&space;\right&space;|+c$

$12)\int&space;\frac{dx}{\sqrt{x^{2}+a}}=ln\left&space;|&space;x+\sqrt{x+a}&space;\right&space;|+c$

$13)\int&space;\frac{dx}{1+x^{2}}=artgx+c=-arcctgx+c$

$14)\int&space;\frac{dx}{a^{2}+x^{2}}=\frac{1}{a}artg\frac{x}{a}+c&space;,&space;a\neq&space;0$

$15)\int&space;\frac{dx}{\sqrt{1-x^{2}}}=arcsinx+c=-arccosx+c$

$16)\int&space;\frac{dx}{\sqrt{a^{2}-x^{2}}}=arcsin\frac{x}{a}+c,&space;a>0$

$17)\int&space;tgxdx=-ln\left&space;|&space;cosx&space;\right&space;|+c$

$18)\int&space;cotgxdx=ln\left&space;|&space;sinx&space;\right&space;|+c$

$19)\int&space;shxdx=chx+c$

$20)\int&space;chxdx=shx+c$

$21)\int&space;\frac{dx}{ch^{2}x}=thx+c$

$22)\int&space;\frac{dx}{sh^{2}x}=-cthx+c$

##### Vetite e integralit te pacaktuar:

$1)\left&space;(&space;\int&space;f(x)dx&space;\right&space;)'=f(x)$

$2)&space;d\left&space;(&space;\int&space;f(x)dx&space;\right&space;)=f(x)dx$

$3)\int&space;F'(x)dx+F(x)+c$

$4)\int&space;dF(x)=F(x)+c$

$5)\int&space;\left&space;[&space;f(x)\pm&space;g(x)&space;\right&space;]dx=\int&space;f(x)dx\pm&space;\int&space;g(x)dx$

$6)\int&space;kf(x)dx=k\int&space;f(x)dx$