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

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

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integral of 3/(2x)

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

\frac{3}{2} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{3}{2} ln ∣ x ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ x ∣ + C

\frac{d y}{d x} = \frac{x e ^{3 x + y^{3}}}{y ^{2}}

\frac{d}{d x} ((3 x^{3} - 4) (- 4 x - 3))

4 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

\int 1 x d x

y = 19 sin (x) cos (x)