What is the integral of sin(x)sin(x+pi/6) ?

The integral of sin(x)sin(x+pi/6) is 1/4 (-sin(2x+pi/6)+sqrt(3)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)sin(x+pi/6)

\int sin (x) sin (x + \frac{π}{6}) d x

\frac{1}{4} (- sin (2 x + \frac{π}{6}) + 3 x) + C

Solution steps

\int sin (x) sin (x + \frac{π}{6}) d x

Rewrite using trig identities

= \int \frac{1}{4} (- 2 cos (2 x + \frac{π}{6}) + 3) d x

Take the constant out:

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

= \frac{1}{4} \cdot \int - 2 cos (2 x + \frac{π}{6}) + 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{4} (- \int 2 cos (2 x + \frac{π}{6}) d x + \int 3 d x)

\int 2 cos (2 x + \frac{π}{6}) d x = sin (2 x + \frac{π}{6})

\int 3 d x = 3 x

= \frac{1}{4} (- sin (2 x + \frac{π}{6}) + 3 x)

Add a constant to the solution

= \frac{1}{4} (- sin (2 x + \frac{π}{6}) + 3 x) + C

\frac{\partial}{\partial x} (6 x^{2} cos (y^{7}))

y = \frac{8 x ^{2} + 6 x + 2}{x}

\int_{1}^{5} 5 d x

x \to 0 lim (\frac{1}{x + 2})

x \to 0 + lim (x^{3})

What is the integral of sin(x)sin(x+pi/6) ?
The integral of sin(x)sin(x+pi/6) is 1/4 (-sin(2x+pi/6)+sqrt(3)x)+C