Primitive Elementari

---

Index

1. Primitive Elementari
2. Esempi

Related

• Primitive
• Integrali
• Calcolo Integrale (class)

---

Primitive Elementari

$f(x)$	F(x)
$\cos x$	$\sin x$
$\sin x$	$-\cos x$
$e^x$	$e^x$
$e^{\alpha x}$	$\frac{e^{\alpha x}}{\alpha }$
$a^x$	$\frac{a^x}{\ln a}$
$x^n$	$\frac{x^{n+1}}{n+1}\forall n\ne -1$
$\frac{1}{x}$	$\ln \mid x\mid$
$\frac{1}{1+x^2}$	$\text{arctg}x$
$\frac{1}{{\cos }^{2}x}$	$\tan x$

Sono le inverse delle Derivate

---

Esempi

es1

$\int x^{7}dx=\{\frac{x^8}{8}+c\}$

es2

$\int x^{-3}dx=\{\frac{x^{-2}}{-2}+c\}$

es3

${\int }_{-7}^{-5}\frac{1}{x}dx=\ln (|x|){|}_{-7}^{-5}=\ln (5)-\ln (7)$

es4

${\int }_{\frac{1}{{\cos }^{2}x}}dx=\{\tan (x)+c\}$

---