What is the integral of (x^3)/(xln(x)) ?

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

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integral of (x^3)/(xln(x))

\int \frac{x ^{3}}{x ln ( x )} d x

Ei (3 ln (x)) + C

Solution steps

\int \frac{x ^{3}}{x ln ( x )} d x

Cancel the common factor:

x

= \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

x \to 0 + lim (e^{\frac{1}{x}})

\int e^{- 3 t} d t

\frac{\partial}{\partial x} (z \cdot e^{x yz})

y^{^{'}} = 6 x y^{2}

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

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