What is the integral of 1/(3x+2xln(x)) ?

The integral of 1/(3x+2xln(x)) is 1/2 ln|3+2ln(x)|+C

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integral of 1/(3x+2xln(x))

\int \frac{1}{3 x + 2 x ln ( x )} d x

\frac{1}{2} ln ∣ 3 + 2 ln (x) ∣ + C

Solution steps

\int \frac{1}{3 x + 2 x ln ( x )} d x

Apply u-substitution

: \int \frac{1}{3 + 2 u} d u

= \int \frac{1}{3 + 2 u} d u

Apply u-substitution

: \int \frac{1}{2 v} d v

= \int \frac{1}{2 v} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} ln ∣ v ∣

Substitute back

= \frac{1}{2} ln ∣ 3 + 2 ln (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 3 + 2 ln (x) ∣ + C

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

\int \frac{2}{πn} sin (\frac{n x π}{2}) d x

\int_{0}^{1} \frac{17}{4 x - 1} d x

ln (1 - 4 y)

\frac{\partial}{\partial x} (cos (8 x) sin (4 y))

What is the integral of 1/(3x+2xln(x)) ?
The integral of 1/(3x+2xln(x)) is 1/2 ln|3+2ln(x)|+C