Primitive Function

9000065503

Level: 
A
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int (4x^{-3} - x^{-4})\, \mathrm{d}x \]
\(- 2x^{-2} + \frac{1} {3}x^{-3} + c,\ c\in \mathbb{R}\)
\(-\frac{4} {3}x^{-2} -\frac{1} {3}x^{-3} + c,\ c\in \mathbb{R}\)
\(-\frac{3} {4}x^{-4} -\frac{1} {5}x^{-5} + c,\ c\in \mathbb{R}\)
\(- 12x^{2} + 4x^{-3} + c,\ c\in \mathbb{R}\)

9000065504

Level: 
B
Evaluate the following integral on the interval \((0;+\infty)\). \[ \int (1 -\sqrt{x})(1 + \sqrt{x})\, \mathrm{d}x \]
\(x -\frac{1} {2}x^{2} + c,\ c\in \mathbb{R}\)
\((x -\frac{1} {2}x^{2})(x + \frac{1} {2}x^{2}) + c,\ c\in \mathbb{R}\)
\(x -\frac{1} {2}x^{\frac{1} {2} } + c,\ c\in \mathbb{R}\)
\((x -\frac{1} {2}x^{-\frac{1} {2} })(x + \frac{1} {2}x^{-\frac{1} {2} }) + c,\ c\in \mathbb{R}\)