integral of (sin(x))/(sqrt(5cos(x)+10))

解答

\int \frac{sin ( x )}{5 cos ( x ) + 10} d x

- \frac{2}{5} 5 cos (x) + 10 + C

求解步骤

\int \frac{sin ( x )}{5 cos ( x ) + 10} d x

使用换元积分法

= \int - \frac{1}{5 u} d u

提出常数:

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

= - \frac{1}{5} \cdot \int \frac{1}{u} d u

使用幂法则

= - \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

u = 5 cos (x) + 10

代回

= - \frac{1}{5} \cdot 2 (5 cos (x) + 10)^{\frac{1}{2}}

化简

- \frac{1}{5} \cdot 2 (5 cos (x) + 10)^{\frac{1}{2}} : - \frac{2}{5} 5 cos (x) + 10

= - \frac{2}{5} 5 cos (x) + 10

解答补常数

= - \frac{2}{5} 5 cos (x) + 10 + C

\frac{\partial}{\partial x} (\frac{x}{x - y})

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

\frac{\partial}{\partial x} (x^{2} - ln (x y))

\frac{d}{d x} (π csc (π + \frac{x ^{6}}{3}))

d er i v a t i v e f (x) = (x - 1)