\( (\sec^2 y- 1)dy = \sin^2 x \sin x dx \)

\( \int{(\sec^2 y- 1)dy} = \int{\sin^2 x \sin x dx}\)

\( \tan y - y = \int{(1- \cos^2 x )( \sin x )}\)

\( \tan y - y = \int{ \sin x dx }- \int{\cos^2 x \sin x dx} \)

\( \tan y - y + c= -cos x + \frac{ \cos^3 x}{3} \)