[tex] \int\limits \, \sqrt[3]{(3x^2-1)^2xdx} [/tex] помогите решить интеграл. Created by fen9oops. algebra-ru

tex] помогите решить интеграл...

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[tex] \int\limits \, \sqrt[3]{(3x^2-1)^2xdx} [/tex]
помогите решить интеграл

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$\int \sqrt[3]{(3x^2-1)^2}\, x\, dx=[\, t=3x^2-1,\; dt=6x\, dx\, ]=\\\\=\frac{1}{6}\int \sqrt[3]{t^2}dt=\frac{1}{6}\int t^{\frac{2}{3}}dt=\frac{1}{6}*\frac{t^{\frac{5}{3}}}{\frac{5}{3}}+C=\frac{3}{30}\sqrt[3]{(3x^2-1)^5}+C$

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