Primitive

Exerciții și probleme... primitive.

1. Calculați următoarele integrale nedefinite:

 a) $\displaystyle \int 3 dx$, $x \in \mathbb{R}$ b) $\displaystyle \int x^5 dx$, $x \in \mathbb{R}$ c) $\displaystyle \int \frac{1}{x^3} dx$, $x \in (0, \infty)$ d) $\displaystyle \int \sqrt[4]{ x } dx$, $x \in (0, \infty)$ e) $\displaystyle \int \sqrt[5]{ x^{3} } dx$, $x \in (0, \infty)$ f) $\displaystyle \int 7^x dx$, $x \in \mathbb{R}$ g) $\displaystyle \int \frac{1}{x^2 + 9} dx$, $x \in \mathbb{R}$ h) $\displaystyle \int \frac{1}{x^2 - 4} dx$, $x \in (2, \infty)$ i) $\displaystyle \int \frac{1}{ \sqrt{x^2 + 25} } dx$, $x \in \mathbb{R}$ j) $\displaystyle \int \frac{1}{ \sqrt{x^2 - 16} } dx$, $x \in (4, \infty)$ k) $\displaystyle \int \frac{1}{ \sqrt{49 - x^2} } dx$, $x \in (-7, 7)$ l) $\displaystyle \int 1 dx$, $x \in \mathbb{R}$; $\displaystyle \int x dx$, $x \in \mathbb{R}$; $\displaystyle \int \frac{1}{x} dx$, $x \in \mathbb{R} \setminus \{ 0 \}$; $\displaystyle \int \sqrt{x} dx$, $x \in (0, \infty)$; $\displaystyle \int e^{x} dx$, $x \in \mathbb{R}$; $\displaystyle \int \sin{x} dx$, $x \in \mathbb{R}$; $\displaystyle \int \cos{x} dx$, $x \in \mathbb{R}$; $\displaystyle \int \text{tg}{x} dx$, $\displaystyle x \in (\frac{-\pi}{2}, \frac{\pi}{2})$; $\displaystyle \int \text{ctg}{x} dx$, $x \in (0, \pi)$; $\displaystyle \int \frac{1}{\cos^2{x}} dx$, $\displaystyle x \in (\frac{-\pi}{2}, \frac{\pi}{2})$; $\displaystyle \int \frac{1}{\sin^2{x}} dx$, $x \in (0, \pi)$.