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) | \( \displaystyle \int 1 dx \), \( x \in \mathbb{R} \); \( \displaystyle \int x dx \), \( x \in \mathbb{R} \); \( \displaystyle \int \frac{1}{x} dx \), \( x \in \mathbb{R} \setminus \{ 0 \} \); \( \displaystyle \int \sqrt{x} dx \), \( x \in (0, \infty) \); \( \displaystyle \int e^{x} dx \), \( x \in \mathbb{R} \); \( \displaystyle \int \sin{x} dx \), \( x \in \mathbb{R} \); \( \displaystyle \int \cos{x} dx \), \( x \in \mathbb{R} \); \( \displaystyle \int \text{tg}{x} dx \), \( \displaystyle x \in (\frac{-\pi}{2}, \frac{\pi}{2}) \); \( \displaystyle \int \text{ctg}{x} dx \), \( x \in (0, \pi) \); \( \displaystyle \int \frac{1}{\cos^2{x}} dx \), \( \displaystyle x \in (\frac{-\pi}{2}, \frac{\pi}{2}) \); \( \displaystyle \int \frac{1}{\sin^2{x}} dx \), \( x \in (0, \pi) \). |