0-1-3x-2-1-1-x-x-3-dx-

Question Number 131147 by EDWIN88 last updated on 02/Feb/21

\int_{0}^{1} \frac{3 x^{2} - 1}{1 + \sqrt{x - x^{3}}} d x = ?

Commented by EDWIN88 last updated on 02/Feb/21

\sqrt{x - x^{3}} = w - 1 \Rightarrow x - x^{3} = {(w - 1)}^{2}

(1 - 3 x^{2}) d x = 2 (w - 1) d w

I = - \int_{1}^{1} \frac{2 w - 1}{w} d w = \int_{1}^{1} (\frac{1}{w} - 2) d w

= {[\ln ∣ w ∣ - 2 w]}_{1}^{1}

= - 2 - (- 2) = 0

Answered by Ar Brandon last updated on 02/Feb/21

Let u = x - x^{3} then du = - ({3 x}^{2} - 1) dx