What is the integral of (x^2)/(ln(x)) ?

The integral of (x^2)/(ln(x)) is \Ei(3ln(x))+C

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integral of (x^2)/(ln(x))

\int \frac{x ^{2}}{ln ( x )} d x

Ei (3 ln (x)) + C

Solution steps

\int \frac{x ^{2}}{ln ( x )} d x

Apply u-substitution

: \int \frac{e ^{3 u}}{u} d u

= \int \frac{e ^{3 u}}{u} d u

Apply u-substitution

: \int \frac{e ^{v}}{v} d v

= \int \frac{e ^{v}}{v} d v

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (v)

Substitute back

= Ei (3 ln (x))

Add a constant to the solution

= Ei (3 ln (x)) + C

ln (x^{2})

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

\int 2^{2 x} e^{x} d x

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

\int (\frac{3 x + 3}{x ^{2} + 8 x + 16}) d x

What is the integral of (x^2)/(ln(x)) ?
The integral of (x^2)/(ln(x)) is \Ei(3ln(x))+C