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

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

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

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

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

Solution steps

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

\int \frac{1}{2} d x = \frac{1}{2} x

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

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

Add a constant to the solution

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

\int_{1}^{2} (x^{4} + \frac{1}{4 x ^{4}}) d x

x^{4} - 2 x^{4}

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

\int - 3 x e^{- 3 x} d x

x = 0 \sum \infty \frac{x}{5 ^{x}}

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