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

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

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integral of cos(2x+y)

\int cos (2 x + y) d x

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

Solution steps

\int cos (2 x + y) d x

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= \int cos (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 cos (u) d u

Use the common integral:

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

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

Substitute back

u = y + 2 x

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

Add a constant to the solution

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

\int_{1}^{2} 8 x^{3} + 3 x^{2} d x

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\frac{\partial}{\partial x} (1 + e^{2 x})

\int_{- 1}^{3} (t + 2) (t^{2} - 2 t + 4) d t

e^{- x}, 0.25

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