What is the integral of sin(2x+y) ?

The integral of sin(2x+y) is -1/2 cos(y+2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin(2x+y)

integral

sin (2 x + y)

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

Solution steps

\int sin (2 x + y) d x

Apply u-substitution

= \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{2} (- cos (u))

Substitute back

u = y + 2 x

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

Simplify

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

Add a constant to the solution

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

in t e g r a l f (x) = 55 - 4 x

in t e g r a l \frac{2 x}{( x + 1 ) ^{2}}

in t e g r a l \frac{( x + 8 )}{x + 7}

in t e g r a l \frac{1}{x ^{2} + y ^{2}}

in t e g r a l \frac{( 1 + x ^{2} )}{( 1 - x ^{3} )}

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