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

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