integral of x^2e^{x^3-1}

解答

\int x^{2} e^{x^{3} - 1} d x

\frac{1}{3} e^{x^{3} - 1} + C

求解步骤

\int x^{2} e^{x^{3} - 1} d x

使用换元积分法

= \int \frac{e ^{u}}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= \frac{1}{3} e^{u}

u = x^{3} - 1

代回

= \frac{1}{3} e^{x^{3} - 1}

解答补常数

= \frac{1}{3} e^{x^{3} - 1} + C

x \to \frac{1}{2} lim (10 x^{2} - 9 x + 2)

\int_{1}^{\infty} \frac{1}{x} d x

s l o p e in t erce pt (0, 2), (- 5, - 1)

in v erse l a pl a ce e^{- s} \frac{1}{s - 4}

x \to \infty + lim (\frac{2 x + 1}{4 x ^{2} + x})