integral of (sin(x))/(sqrt(4-cos(x)))

解答

\int \frac{sin ( x )}{4 - cos ( x )} d x

2 4 - cos (x) + C

求解步骤

\int \frac{sin ( x )}{4 - cos ( x )} d x

使用换元积分法

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

使用幂法则

= 2 u^{\frac{1}{2}}

u = 4 - cos (x)

代回

= 2 (4 - cos (x))^{\frac{1}{2}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

= 2 4 - cos (x)

解答补常数

= 2 4 - cos (x) + C

\int 4 x - 4 x^{2} d x

\frac{d}{d x} (arcsin (3 x^{4}))

\frac{d y}{d x} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}, y (0) = - 1

\int \frac{t ^{2}}{2} d t

\int \frac{1}{( x ^{2} - 5 ) ^{\frac{3}{2}}} d x