What is the integral of (sin(x))/(sqrt(5cos(x)+10)) ?

The integral of (sin(x))/(sqrt(5cos(x)+10)) is -2/5 sqrt(5cos(x)+10)+C

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

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 5 cos (x) + 10

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

Simplify

- \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

Add a constant to the solution

= - \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}))

f (x) = (x - 1)

What is the integral of (sin(x))/(sqrt(5cos(x)+10)) ?
The integral of (sin(x))/(sqrt(5cos(x)+10)) is -2/5 sqrt(5cos(x)+10)+C