Este corectă rezolvarea?

[tex] \int( \frac{1}{3 + {x}^{2} } - \frac{1}{ \sqrt{3 + {x}^{2} } } ) \: dx,x\:\in\:\mathbb{R}[/tex]

[tex] = \int \frac{1}{3 + {x}^{2} } \: dx - \int \frac{1}{ \sqrt{3 + {x}^{2} } } \: dx[/tex]

[tex] = \int\frac{1}{ {( \sqrt{3} )}^{2} + {x}^{2} } \: dx - \int \frac{1}{ \sqrt{ {( \sqrt{3} )}^{2} + {x}^{2} } } \: dx[/tex]

[tex] = \frac{1}{ \sqrt{3} } \: arctg \: \frac{x}{ \sqrt{3} } - ln(x + \sqrt{ {x}^{2} + {( \sqrt{3}) }^{2} } ) [/tex]

[tex] = \frac{1}{ \sqrt{3} } \: arctg \: \frac{x}{ \sqrt{3} } - ln(x + \sqrt{ {x}^{2} + 3 } ) + C[/tex]