If ∫$$1x1$$−$$x3dx=alog$$⁡$$1$$−$$x3$$−$$11$$−$$x3+1+b$$, then a is equal to

Question

If ∫$$1x1$$−$$x3dx=alog$$⁡$$1$$−$$x3$$−$$11$$−$$x3+1+b$$, then a is equal  to

Infinity Learn · Accepted Answer

Let $$1$$−$$x3=y2$$.  Then −$$3x2dx=2ydy$$∴∫$$1x1$$−$$x3dx=$$∫$$x2dxx31$$−$$x3$$                                $$=$$−$$23$$∫$$ydy1$$−$$y2y$$                               $$=13logy$$−$$1y+1+C$$                               $$=13log1$$−$$x3$$−$$11$$−$$x3+1+C$$∴$$a=13$$

$\begin{array}{l} If \int \frac{1}{x \sqrt{1 - x^{3}}} d x = a \log |\frac{\sqrt{1 - x^{3}} - 1}{\sqrt{1 - x^{3}} + 1}| + b, then a is equal to \end{array}$

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If ∫1x1−x3dx=alog⁡1−x3−11−x3+1+b, then a is equal to

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$\begin{array}{l} If \int \frac{1}{x \sqrt{1 - x^{3}}} d x = a \log |\frac{\sqrt{1 - x^{3}} - 1}{\sqrt{1 - x^{3}} + 1}| + b, then a is equal to \end{array}$