integral of \sqrt[7]{x^3}

解答

\int 7 x^{3} d x

\frac{7}{10} x^{\frac{10}{7}} + C

求解步骤

\int 7 x^{3} d x

7 x^{3} = x^{\frac{3}{7}},

假定

x \geq 0

= \int x^{\frac{3}{7}} d x

使用幂法则

= \frac{7}{10} x^{\frac{10}{7}}

解答补常数

= \frac{7}{10} x^{\frac{10}{7}} + C

\frac{d}{d x} (\frac{x ^{2} + 3}{( x - 1 ) ^{3} + ( x + 1 ) ^{3}})

s l o p e (6, - 5), (2, 3)

t an g e n t f (x) = (\frac{x - 3}{x + 3})^{2}, at x = - 2

y^{^{''}} + 7 y^{^{'}} + 10 y = - 18 t e^{3 t}

\int 4 e^{6 x} d x