integral of \sqrt[3]{8x^2}

解答

\int 3 8 x^{2} d x

\frac{6}{5} x^{\frac{5}{3}} + C

求解步骤

\int 3 8 x^{2} d x

使用分布积分法

= 2 x 3 x^{2} - \int \frac{4 x ^{2}}{3 ( x ^{2} ) ^{\frac{2}{3}}} d x

\int \frac{4 x ^{2}}{3 ( x ^{2} ) ^{\frac{2}{3}}} d x = \frac{4}{5} x^{\frac{5}{3}}

= 2 x 3 x^{2} - \frac{4}{5} x^{\frac{5}{3}}

化简

2 x 3 x^{2} - \frac{4}{5} x^{\frac{5}{3}} : \frac{6}{5} x^{\frac{5}{3}}

= \frac{6}{5} x^{\frac{5}{3}}

解答补常数

= \frac{6}{5} x^{\frac{5}{3}} + C

\frac{d}{d x} (6^{5 x^{4} - 10 x^{3} + 5})

d er i v a t i v e 7 + 6 f (x)

\int \frac{x}{x ^{2} - 2 x + 5} d x

d er i v a t i v e y = \frac{7}{x ^{2} + 3}

\frac{\partial}{\partial x} (- y - \frac{x}{y ^{2}})