3x-5-3x-2-10x-2-1-3-dx-Solve-it-without-substitution-method-

Question Number 146689 by naka3546 last updated on 15/Jul/21

\int \frac{- 3 x + 5}{\sqrt[3]{{(3 x^{2} - 10 x)}^{2}}} d x = \dots ?

S o l v e i t w i t h o u t s u b s t i t u t i o n m e t h o d .

Answered by Ar Brandon last updated on 15/Jul/21

I = \int \frac{- 3 x + 5}{\sqrt[3]{{({3 x}^{2} - 10 x)}^{2}}} dx

= - \frac{1}{2} \int \frac{6 x - 10}{\sqrt[3]{{({3 x}^{2} - 10 x)}^{2}}} dx

= - \frac{1}{2} \int \frac{d ({3 x}^{2} - 10 x)}{\sqrt[3]{{({3 x}^{2} - 10 x)}^{2}}}

= - \frac{3}{2} \sqrt[3]{{3 x}^{2} - 10 x} + C

Commented by naka3546 last updated on 15/Jul/21

t h a n k y o u, s i r .