integral of (2x+1)^{5/6}

解答

\int (2 x + 1)^{\frac{5}{6}} d x

\frac{3}{11} (2 x + 1)^{\frac{11}{6}} + C

求解步骤

\int (2 x + 1)^{\frac{5}{6}} d x

使用换元积分法

= \int \frac{u ^{\frac{5}{6}}}{2} d u

提出常数:

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

= \frac{1}{2} \cdot \int u^{\frac{5}{6}} d u

使用幂法则

= \frac{1}{2} \cdot \frac{6}{11} u^{\frac{11}{6}}

u = 2 x + 1

代回

= \frac{1}{2} \cdot \frac{6}{11} (2 x + 1)^{\frac{11}{6}}

化简

\frac{1}{2} \cdot \frac{6}{11} (2 x + 1)^{\frac{11}{6}} : \frac{3}{11} (2 x + 1)^{\frac{11}{6}}

= \frac{3}{11} (2 x + 1)^{\frac{11}{6}}

解答补常数

= \frac{3}{11} (2 x + 1)^{\frac{11}{6}} + C

\frac{\partial}{\partial x} (32 x + 13 y + 90)

\frac{d}{d t} (ln (a + v (t) t))

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

y^{^{'}} = 0.5 y, y (2) = 100

x \to - 1 lim (\frac{∣ x + 1 ∣}{x + 1})