What is the integral of sin(6x)sin(5x) ?

The integral of sin(6x)sin(5x) is 1/2 (-1/11 sin(11x)+sin(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(6x)sin(5x)

\int sin (6 x) sin (5 x) d x

\frac{1}{2} (- \frac{1}{11} sin (11 x) + sin (x)) + C

Solution steps

\int sin (6 x) sin (5 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (- cos (11 x) + cos (x)) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int - cos (11 x) + cos (x) 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}{2} (- \int cos (11 x) d x + \int cos (x) d x)

\int cos (11 x) d x = \frac{1}{11} sin (11 x)

\int cos (x) d x = sin (x)

= \frac{1}{2} (- \frac{1}{11} sin (11 x) + sin (x))

Add a constant to the solution

= \frac{1}{2} (- \frac{1}{11} sin (11 x) + sin (x)) + C

x \to \frac{1}{2} - lim (\frac{1}{2 x - 1})

\frac{d}{d x} (ln (\frac{x ^{2}}{x + 1}))

f (x) = (3 a + 1)^{2}

x \to + 6 lim (36 - x^{2})

x \to + 1 lim (e^{x^{2} - x})

What is the integral of sin(6x)sin(5x) ?
The integral of sin(6x)sin(5x) is 1/2 (-1/11 sin(11x)+sin(x))+C