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

The integral of ((1-cos(x)))/x is ln|x|-\Ci(x)+C

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

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

ln ∣ x ∣ - Ci (x) + C

Solution steps

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

Expand

\frac{1 - cos ( x )}{x} : \frac{1}{x} - \frac{cos ( x )}{x}

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{cos ( x )}{x} d x = Ci (x)

= ln ∣ x ∣ - Ci (x)

Add a constant to the solution

= ln ∣ x ∣ - Ci (x) + C

What is the integral of ((1-cos(x)))/x ?
The integral of ((1-cos(x)))/x is ln|x|-\Ci(x)+C