integral of 1/(\sqrt[5]{x^2)}

解答

\int \frac{1}{5 x ^{2}} d x

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

求解步骤

\int \frac{1}{5 x ^{2}} d x

5 x^{2} = x^{\frac{2}{5}},

假定

x \geq 0

= \int \frac{1}{x ^{\frac{2}{5}}} d x

使用幂法则

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

解答补常数

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

d er i v a t i v e f (x) = (6 x + 1)^{2}

\frac{d}{d x} (ln (8 x))

2 \cdot x \cdot y \cdot y^{^{'}} = - (x^{2} + y^{2})

\frac{d}{d x} (\frac{x ^{2}}{( x ^{2} + 5 ) ^{3}})

t an g e n t 9 y^{7} + 4 x^{3} = 8 y + 5 x, (1, 1)