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

The integral of cos(x)1/x is d\Ci(x)+C

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integral of cos(x)1/x

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

d Ci (x) + C

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Use the nonelementary integral:

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

= d Ci (x)

Add a constant to the solution

= d Ci (x) + C

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