What is the integral from e to ln(x) of ln(x) ?

The integral from e to ln(x) of ln(x) is ln(x)ln(ln(x))-ln(x)

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integral from e to ln(x) of ln(x)

\int_{e}^{l n (x)} ln (x) d x

ln (x) ln (ln (x)) - ln (x)

Solution steps

\int_{e}^{l n (x)} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{e}^{l n (x)}

= [x ln (x) - \int 1 d x]_{e}^{l n (x)}

\int 1 d x = x

= [x ln (x) - x]_{e}^{l n (x)}

Compute the boundaries:

ln (x) ln (ln (x)) - ln (x)

= ln (x) ln (ln (x)) - ln (x)

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\int_{0}^{1} π (x e^{x})^{2} d x

\int_{1.2}^{5.4} 1.6 x e^{\frac{x}{3}} d x

What is the integral from e to ln(x) of ln(x) ?
The integral from e to ln(x) of ln(x) is ln(x)ln(ln(x))-ln(x)