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

The integral of sin(pi+2y)-sin(2y) is ysin(pi+2y)+ysin(2y)+cos(2y)+C

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integral of sin(pi+2y)-sin(2y)

\int sin (π + 2 y) - sin (2 y) d y

y sin (π + 2 y) + y sin (2 y) + cos (2 y) + C

Solution steps

\int sin (π + 2 y) - sin (2 y) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (π + 2 y) d y - \int sin (2 y) d y

\int sin (π + 2 y) d y = y sin (π + 2 y) + y sin (2 y) + \frac{1}{2} cos (2 y)

\int sin (2 y) d y = - \frac{1}{2} cos (2 y)

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

Simplify

y sin (π + 2 y) + y sin (2 y) + \frac{1}{2} cos (2 y) - (- \frac{1}{2} cos (2 y)) : y sin (π + 2 y) + y sin (2 y) + cos (2 y)

= y sin (π + 2 y) + y sin (2 y) + cos (2 y)

Add a constant to the solution

= y sin (π + 2 y) + y sin (2 y) + cos (2 y) + C

\frac{\partial}{\partial y} (x y e^{y} + e^{y} sin (x))

\frac{\partial}{\partial x} (16 - x^{2} - y^{2})

y = e^{- 2 x} + 1, y = 0, x = 0, x = 3

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})

f (x) = x^{6 x}

What is the integral of sin(pi+2y)-sin(2y) ?
The integral of sin(pi+2y)-sin(2y) is ysin(pi+2y)+ysin(2y)+cos(2y)+C