y^'=((ln^2(x)))/(\sqrt[3]{x)}

解

y^{^{'}} = \frac{( ln ^{2} ( x ) )}{3 x}

y = 27 (\frac{1}{18} x^{\frac{2}{3}} ln^{2} (x) - \frac{1}{6} x^{\frac{2}{3}} ln (x) + \frac{1}{4} x^{\frac{2}{3}}) + c_{1}

解答ステップ

y^{'} (x) = \frac{( ln ^{2} ( x ) )}{3 x}

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

y = \int \frac{ln ^{2} ( x )}{3 x} d x

\int \frac{ln ^{2} ( x )}{3 x} d x = 27 (\frac{1}{18} x^{\frac{2}{3}} ln^{2} (x) - \frac{1}{6} x^{\frac{2}{3}} ln (x) + \frac{1}{4} x^{\frac{2}{3}}) + c_{1}

y = 27 (\frac{1}{18} x^{\frac{2}{3}} ln^{2} (x) - \frac{1}{6} x^{\frac{2}{3}} ln (x) + \frac{1}{4} x^{\frac{2}{3}}) + c_{1}