What is the integral of sin(x+3)cos(1-2x) ?

The integral of sin(x+3)cos(1-2x) is 1/2 (cos(-x+4)-1/3 cos(3x+2))+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+3)cos(1-2x)

\int sin (x + 3) cos (1 - 2 x) d x

\frac{1}{2} (cos (- x + 4) - \frac{1}{3} cos (3 x + 2)) + C

Solution steps

\int sin (x + 3) cos (1 - 2 x) d x

Use the following identity:

cos (t) sin (s) = \frac{sin ( s + t ) + sin ( s - t )}{2}

= \int \frac{sin ( x + 3 + 1 - 2 x ) + sin ( x + 3 - ( 1 - 2 x ) )}{2} 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 sin (x + 3 + 1 - 2 x) + sin (x + 3 - (1 - 2 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 sin (x + 3 + 1 - 2 x) d x + \int sin (x + 3 - (1 - 2 x)) d x)

\int sin (x + 3 + 1 - 2 x) d x = cos (- x + 4)

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

= \frac{1}{2} (cos (- x + 4) - \frac{1}{3} cos (3 x + 2))

Add a constant to the solution

= \frac{1}{2} (cos (- x + 4) - \frac{1}{3} cos (3 x + 2)) + C

n = 2 \sum \infty \frac{7}{1 0 ^{n - 1}}

n = 1 \sum \infty \frac{5}{3 ^{- n}}

\frac{d}{d x} (\frac{4}{x ^{10}})

f (x) = e^{\frac{2}{x}}

y = arctan (\frac{4 x}{3})

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