Question

sa se rezolve următoarea:

Answer 1

Explicație pas cu pas:

notăm

1 - x⁵ = u

$- 5 {x}^{4} \ dx = du \implies dx = - \dfrac{du}{5 {x}^{4}} \\ \iff {x}^{4} \ dx = - \dfrac{du}{5}$

$= \int \Big( - \dfrac{ {u}^{5} }{5}\Big) du = - \frac{1}{5} \int {u}^{5} \ du = - \dfrac{1}{5} \cdot \dfrac{{u}^{6}}{6} = - \dfrac{{u}^{6}}{30}$

=>

$\int {x}^{4} {(1 - {x}^{5} )}^{5} dx = - \dfrac{{(1 - {x}^{5})}^{6}}{30} + C = \\ = - \dfrac{{({x}^{5} - 1)}^{6}}{30} + C$