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

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

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integral of sin(2x+y)

\int sin (2 x + y) d x

- \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

= \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

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f (x) = \frac{x}{4}

\int \frac{2 x ^{2} - 4}{x} d x

\int (1 - x^{- 0.52}) d x

\frac{\partial}{\partial x} (5 ln (\frac{3 x y}{7 z}))

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