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受欢迎的微积分 >

integral of e^{2sin(3x)}cos(3x)

解答

\int e^{2 s i n (3 x)} cos (3 x) d x

解答

\frac{1}{6} e^{2 s i n (3 x)} + C

求解步骤

\int e^{2 s i n (3 x)} cos (3 x) d x

使用换元积分法

= \int e^{2 s i n (u)} cos (u) \frac{1}{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^{2 s i n (u)} cos (u) d u

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

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

= \frac{1}{3} \cdot \frac{1}{2} e^{v}

代回

= \frac{1}{3} \cdot \frac{1}{2} e^{2 s i n (3 x)}

化简

\frac{1}{3} \cdot \frac{1}{2} e^{2 s i n (3 x)} : \frac{1}{6} e^{2 s i n (3 x)}

= \frac{1}{6} e^{2 s i n (3 x)}

解答补常数

= \frac{1}{6} e^{2 s i n (3 x)} + C

作图

流行的例子

(\partial)/(\partial x)(2y^{1/2}x^{1/2})

\frac{\partial}{\partial x} (2 y^{\frac{1}{2}} x^{\frac{1}{2}})

f (x) = \frac{10}{x}

limit as x approaches 2 of (x^2)/(x^2-4)

x \to 2 lim (\frac{x ^{2}}{x ^{2} - 4})

derivative of cos(xdx)

\frac{d}{d x} (cos (x) d x)

integral of-4sin(2t-pi/2)

\int - 4 sin (2 t - \frac{π}{2}) d t