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

The integral of 3/(2-x/2) is -6ln|2-x/2 |+C

Popular >

integral of 3/(2-x/2)

\int \frac{3}{2 - \frac{x}{2}} d x

- 6 ln 2 - \frac{x}{2} + C

Solution steps

\int \frac{3}{2 - \frac{x}{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{2 - \frac{x}{2}} d x

Apply u-substitution

: \int - \frac{2}{u} d u

= 3 \cdot \int - \frac{2}{u} d u

Take the constant out:

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

= 3 (- 2 \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 (- 2 ln ∣ u ∣)

Substitute back

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

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

Simplify

= - 6 ln 2 - \frac{x}{2}

Add a constant to the solution

= - 6 ln 2 - \frac{x}{2} + C

\int x^{2} + 2 x + 50 d x

\int \frac{e ^{4 x}}{e ^{4 x}} d x

\int \frac{x - 1}{3 x ^{2} - 6 x + 2} d x

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

\int e^{- x} sin (x) cos (x) d x