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受欢迎的微积分 >

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

解答

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

解答

6 e^{x} + C

求解步骤

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

提出常数:

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

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

使用换元积分法

= 3 \cdot \int 2 e^{u} d u

提出常数:

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

= 3 \cdot 2 \cdot \int e^{u} d u

使用积分常见定则:

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

= 3 \cdot 2 e^{u}

u = x

代回

= 3 \cdot 2 e^{x}

化简

= 6 e^{x}

解答补常数

= 6 e^{x} + C

作图

流行的例子

derivative of 3(5-9x^5)

\frac{d}{d x} (3 (5 - 9 x)^{5})

integral of sec(t)(sec(t)tan(t))

\int sec (t) (sec (t) tan (t)) d t

limit as x approaches infinity of (1+6x)^{3/x}

x \to \infty lim ((1 + 6 x)^{\frac{3}{x}})

integral of x/(sqrt(4x^2+1))

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

(dy)/(dx)=xsqrt(y)cos^2(sqrt(y))

\frac{d y}{d x} = x y cos^{2} (y)