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

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

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integral of xln(ln(x))

\int x ln (ln (x)) d x

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

Solution steps

\int x ln (ln (x)) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

x \to 0 lim ((1 - \frac{x}{3})^{\frac{1}{x}})

arctan (- 2 x)

y^{^{''}} + b y^{^{'}} = 0

x^{2}, x^{2} - 4 x + 4, 0, 2

\int 2 - \frac{1}{x} d x

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