Odpowiedź:
a)
[tex]\int \left((m + 1)x^4 - \frac{m+2}{x} + 2\right)dx = \int \left(9x^4 - \frac{10}{x} + 2\right)dx = 9\int x^4dx - 10 \int \frac{1}{x}dx + 2 \int 1dx = \frac{9x^5}{5}-10 \ln x + 2x + C[/tex]
b)
[tex]\int \frac{x+m+1}{x^2}dx = \int \frac{x+9}{x^2}dx = \int \left(\frac{x}{x^2} + \frac{9}{x^2}\right)dx = \int \left(\frac{1}{x} + \frac{9}{x^2}\right)dx = \int \frac{1}{x}dx + \int \frac{9}{x^2}dx = \int \frac{1}{x}dx + 9 \int \frac{1}{x^2}dx = \int \frac{1}{x}dx + 9 \int x^{-2}dx = \ln x + 9\cdot \left(-\frac{1}{x}\right) = \ln x - \frac{9}{x} + C[/tex]
c)
[tex]\int \frac{\sqrt{x}}{(m+2)x}dx = \int \frac{\sqrt{x}}{10x}dx = \int \frac{1}{10\sqrt{x}}dx = \frac{1}{10} \int \frac{1}{\sqrt{x}} dx = \frac{1}{10} \int x^{-\frac{1}{2}} dx = \frac{1}{10} \cdot 2\sqrt{x} = \frac{\sqrt{x}}{5} + C[/tex]
