Question

Integrala de la 0 la infinit din 24 /(3x+1) ^5 dx

Answer 1

Răspuns:

2

Explicație pas cu pas:

$\int_{0}^{\infty} \frac{24}{ {(3x + 1)}^{5} } dx = 8\int_{0}^{\infty} \frac{3}{ {(3x + 1)}^{5} } dx =$

$= 8\int_{0}^{\infty} \frac{(3x + 1)'}{ {(3x + 1)}^{5} } dx = 8\times \Big(- \frac{1}{4 {(3x + 1)}^{4} }\Big)\Big|_{0}^{\infty}$

$= \Big(- \frac{2}{{(3x + 1)}^{4} }\Big)\Big|_{0}^{\infty} = 0 - ( - 2) = 2$