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

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

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integral of-1/2 cos(2x)+C

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

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

Solution steps

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

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

\int \frac{1}{2} cos (2 x) d x = \frac{1}{4} sin (2 x)

\int C d x = C x

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

Add a constant to the solution

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

x^{4} e^{6 x}

\frac{d ^{3} y}{d x ^{3}} + \frac{d ^{2} y}{d x ^{2}} - 2 y = 0

\int cos (n) x d x

y = 2 x^{3} - x^{2} + \frac{4}{x}, (4, 1)

x y^{^{''}} + y^{^{'}} = 4 x

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