Răspuns:
2
Explicație pas cu pas:
[tex]\int_{0}^{\infty} \frac{24}{ {(3x + 1)}^{5} } dx = 8\int_{0}^{\infty} \frac{3}{ {(3x + 1)}^{5} } dx = \\ [/tex]
[tex]= 8\int_{0}^{\infty} \frac{(3x + 1)'}{ {(3x + 1)}^{5} } dx = 8\times \Big(- \frac{1}{4 {(3x + 1)}^{4} }\Big)\Big|_{0}^{\infty} \\ [/tex]
[tex]= \Big(- \frac{2}{{(3x + 1)}^{4} }\Big)\Big|_{0}^{\infty} = 0 - ( - 2) = 2 \\ [/tex]
