integral of ((cos(3x)))/(1+sin(3x))

解答

\int \frac{( cos ( 3 x ) )}{1 + sin ( 3 x )} d x

\frac{1}{3} ln ∣ 1 + sin (3 x) ∣ + C

求解步骤

\int \frac{cos ( 3 x )}{1 + sin ( 3 x )} d x

使用换元积分法

= \int \frac{1}{3 u} 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 \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

u = 1 + sin (3 x)

代回

= \frac{1}{3} ln ∣ 1 + sin (3 x) ∣

解答补常数

= \frac{1}{3} ln ∣ 1 + sin (3 x) ∣ + C

\int_{0}^{1} 2 π x (12 - 12 x) d x

d er i v a t i v e e^{4}

y^{^{''}} - \frac{9}{t} y^{^{'}} + \frac{34}{t ^{2}} y = 0

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

\frac{d y}{d x} = \frac{3 x + x y ^{2}}{y + x ^{2} y}