Ответы на вопрос:
Замена cos x = y, dy = -sin x dx, тогда sin^2 x = 1 - cos^2 x = 1 - y^2 корень кубический (cos^2 x) = (cos x)^(2/3) = y^(2/3) int (sin^2 x*sin x dx)/(cos x)^(2/3) = = -int (1 - y^2)/y^(2/3) dy = int (y^2 - 1)*y^(-2/3) dy = int y^(4/3) dy - int y^(-2/3) dy = = 3/7*y^(7/3) - 3y^(1/3) + c = 3/7*(cos x)^(7/3) - 3(cos x)^(1/3) + c
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