integral of (1/(4\sqrt[8]{x^2)})

解答

\int (\frac{1}{4 8 x ^{2}}) d x

\frac{1}{3} x^{\frac{3}{4}} + C

求解步骤

\int \frac{1}{4 8 x ^{2}} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int \frac{1}{8 x ^{2}} d x

8 x^{2} = 4 x,

假定

x \geq 0

= \frac{1}{4} \cdot \int \frac{1}{4 x} d x

使用幂法则

= \frac{1}{4} \cdot \frac{4}{3} x^{\frac{3}{4}}

化简

\frac{1}{4} \cdot \frac{4}{3} x^{\frac{3}{4}} : \frac{1}{3} x^{\frac{3}{4}}

= \frac{1}{3} x^{\frac{3}{4}}

解答补常数

= \frac{1}{3} x^{\frac{3}{4}} + C

d er i v a t i v e f (x) = (3 x + 4) (5 - x^{2}) (4 + x^{2})

x \to \infty lim (e^{x} + 3)

\int_{0}^{\infty} e^{- \frac{x}{4}} d x

x \to 0 lim ((1 + x)^{\frac{2}{x}})

\int 5 tan (6 x) sec^{2} (6 x) d x