Odpowiedź:
Rozwiążemy podane całki nieoznaczone dla m=8
a)
[tex]\int\ ({(8+1)x^4-\frac{8+2}{x}+2) } \, dx =9\int {x^4} \, dx -10\int{\frac{1}{x} } \, dx +2\int {} \, dx =\frac{9x^5}{5} -10ln|x|+2x+C[/tex]
b)
[tex]\int {\frac{x+8+1}{x^2} } \, dx =\int {\frac{x+9}{x^2} } \, dx =\int {\frac{x}{x^2} } \, dx+\int {\frac{9}{x^2} } \, dx =\int {\frac{1}{x} } \, dx+9\int {\frac{1}{x^2} } \, dx =ln|x|-\frac{9}{x} +C[/tex]
c)
[tex]\int {\frac{\sqrt{x} }{(8+2)x} } \, 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 \frac{x^{\frac{1}{2}} }{\frac{1}{2}} =\frac{1}{10} \cdot \frac{\sqrt{x} }{\frac{1}{2} } =\frac{\sqrt{x} }{5} +C[/tex]
