What is the integral of x^{-1}cos(x) ?

The integral of x^{-1}cos(x) is \Ci(x)+C

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integral of x^{-1}cos(x)

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

Ci (x) + C

Solution steps

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

Simplify

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

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

Use the nonelementary integral:

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

= Ci (x)

Add a constant to the solution

= Ci (x) + C