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

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

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integral of x/(xln(x))

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

Ei (ln (x)) + C

Solution steps

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

Apply u-substitution

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

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

Use the nonelementary integral:

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

= Ei (u)

Substitute back

u = ln (x)

= Ei (ln (x))

Add a constant to the solution

= Ei (ln (x)) + C

y^{^{'}} = - y^{2} t - y^{2} t^{2}, y (0) = 3

\int sin (6 x) sin (5 x) d x

x \to \frac{1}{2} - lim (\frac{1}{2 x - 1})

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

f (x) = (3 a + 1)^{2}