integral of (e^{2sqrt(x)})/(3sqrt(x))

解答

\int \frac{e ^{2 x}}{3 x} d x

\frac{1}{3} e^{2 x} + C

求解步骤

\int \frac{e ^{2 x}}{3 x} d x

提出常数:

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

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

使用换元积分法

= \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 = 2 x

代回

= \frac{1}{3} e^{2 x}

解答补常数

= \frac{1}{3} e^{2 x} + C

\frac{d}{d x} (x^{3} - 4 x + 7)

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

\frac{d}{d x} (x^{2} + y^{2} + z^{2})

d er i v a t i v e \frac{5}{4 ( x ^{3} + 2 ) ^{3}}

x \to 4 lim (16)