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

The integral of x/(2ln(x)) is 1/2 \Ei(2ln(x))+C

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integral of x/(2ln(x))

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

\frac{1}{2} Ei (2 ln (x)) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{x}{ln ( x )} d x

Apply u-substitution

: \int \frac{e ^{2 u}}{u} d u

= \frac{1}{2} \cdot \int \frac{e ^{2 u}}{u} d u

Apply u-substitution

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

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

Use the nonelementary integral:

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

= \frac{1}{2} Ei (v)

Substitute back

= \frac{1}{2} Ei (2 ln (x))

Add a constant to the solution

= \frac{1}{2} Ei (2 ln (x)) + C

x \to 1 lim (x + 2)

x \to π lim (ln (cos (x) - 7))

f (x) = \frac{1}{3 x ^{\frac{2}{3}}}

\int x^{5} 1 + x^{2} d x

y^{^{''}} = k y

What is the integral of x/(2ln(x)) ?
The integral of x/(2ln(x)) is 1/2 \Ei(2ln(x))+C