dx-x-1-3-x-2-5-1-4-

Question Number 159315 by cortano last updated on 15/Nov/21

\int \frac{d x}{\sqrt[4]{{(x - 1)}^{3} {(x + 2)}^{5}}} ?

Commented by tounghoungko last updated on 15/Nov/21

Y = \int \frac{d x}{{(x + 2)}^{2} {(\frac{x - 1}{x + 2})}^{3 / 4}}

l e t \sqrt[4]{\frac{x - 1}{x + 2}} = v \Rightarrow x = \frac{2 v^{4} + 1}{1 - v^{4}}

Y = \int \frac{1}{{(\frac{2 v^{4} + 1 + 2 - 2 v^{4}}{1 - v^{4}})}^{2} v^{3}} (\frac{12 v^{3}}{{(1 - v^{4})}^{2}}) d v

Y = \int \frac{12}{9} d v = \frac{4}{3} v + c = \frac{4}{3} \sqrt[4]{\frac{x - 1}{x + 2}} + c