What is the integral of 1/(x/2-3)cos(x/2-3) ?

The integral of 1/(x/2-3)cos(x/2-3) is 2\Ci(x/2-3)+C

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integral of 1/(x/2-3)cos(x/2-3)

\int \frac{1}{\frac{x}{2} - 3} cos (\frac{x}{2} - 3) d x

2 Ci (\frac{x}{2} - 3) + C

Solution steps

\int \frac{1}{\frac{x}{2} - 3} cos (\frac{x}{2} - 3) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{u} d u

= \int \frac{2 cos ( u )}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{cos ( u )}{u} d u

Use the nonelementary integral:

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

= 2 Ci (u)

Substitute back

u = \frac{x}{2} - 3

= 2 Ci (\frac{x}{2} - 3)

Add a constant to the solution

= 2 Ci (\frac{x}{2} - 3) + C

(lo g_{2} (x))^{2}

\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

\frac{\partial}{\partial x} (\frac{x}{y ^{2} + x ^{2}})

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

\int \frac{4 x ^{2} + 1}{4 x} d x

What is the integral of 1/(x/2-3)cos(x/2-3) ?
The integral of 1/(x/2-3)cos(x/2-3) is 2\Ci(x/2-3)+C