What is the integral of (-cos(2x)-1)/4 ?

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

Popular >

integral of (-cos(2x)-1)/4

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

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

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \cdot \int - cos (2 x) - 1 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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\int \frac{3}{98} x^{2} d x

f (x) = cos^{2} (3 x)

y^{^{'}} = 8 x^{3} \cdot y^{2}

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 5 x )})

y^{^{'}} + \frac{1}{x} y - e^{- x^{2}} = 0, y (1) = 0

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