2010008106

Podoblast: 
Primitivní funkce
Část: 
B
Project ID: 
2010008106
Source Problem: 
2010008105
Accepted: 
0
Clonable: 
1
Easy: 
0
Vypočtěte \[ \int \left( \frac{2}{x} + \frac{1}{x+2}+\frac{x}{x^2+1}\right) \mathrm{d}x \] na intervalu \((0;+\infty)\).
\( 2\ln x + \ln(x+2) + \frac12 \ln(x^2+1)+c;~c \in \mathbb{R}\)
\( 2\ln x + \ln(x+2) + \frac12 x^2\ln(x^2+1)+c;~c \in \mathbb{R}\)
\( \frac{4}{x^2} + \frac{1}{\frac12 x^2+2x} + \frac{\frac12x^2}{\frac13x^3+x}+c;~c \in \mathbb{R}\)
\( 2\ln x + \ln(x+2) + \frac{3x}{2(x^2+3)}+c;~c \in \mathbb{R}\)