integral of \sqrt[3]{x}+1/(\sqrt[3]{x)}

解答

\int 3 x + \frac{1}{3 x} d x

\frac{3}{4} x^{\frac{4}{3}} + \frac{3}{2} x^{\frac{2}{3}} + C

求解步骤

\int 3 x + \frac{1}{3 x} d x

使用积分加法定则:

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

= \int 3 x d x + \int \frac{1}{3 x} d x

\int 3 x d x = \frac{3}{4} x^{\frac{4}{3}}

\int \frac{1}{3 x} d x = \frac{3}{2} x^{\frac{2}{3}}

= \frac{3}{4} x^{\frac{4}{3}} + \frac{3}{2} x^{\frac{2}{3}}

解答补常数

= \frac{3}{4} x^{\frac{4}{3}} + \frac{3}{2} x^{\frac{2}{3}} + C

in v erse l a pl a ce \frac{s}{( s + 1 )}

\frac{\partial}{\partial z} (x^{yz})

\frac{d}{d x} (11 arccot (x) + 11 arccot (\frac{1}{x}))

d er i v a t i v e \frac{- 5}{( 2 x ^{3} + 7 ) ^{2}}

s l o p e (2, 7), (- 5, 2)