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

The integral of (cos(2x))/x is \Ci(2x)+C

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integral of (cos(2x))/x

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

Ci (2 x) + C

Solution steps

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

Apply u-substitution

: \int \frac{cos ( u )}{u} d u

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

Use the nonelementary integral:

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

= Ci (u)

Substitute back

u = 2 x

= Ci (2 x)

Add a constant to the solution

= Ci (2 x) + C

\int 2 sin (x) + 5 d x

\frac{e ^{x}}{x - 1}

\int 3 cos (3 t) d t

x \to 2 lim (\frac{2 x - 3}{x + 1})

(3, 1), (- 2, - 2)