What is the integral from 0 to 1 of ln^3(x) ?

The integral from 0 to 1 of ln^3(x) is -6

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integral from 0 to 1 of ln^3(x)

\int_{0}^{1} ln^{3} (x) d x

- 6

Solution steps

\int_{0}^{1} ln^{3} (x) d x

Apply Integration By Parts

= [x ln^{3} (x) - \int 3 ln^{2} (x) d x]_{0}^{1}

\int 3 ln^{2} (x) d x = 3 (x ln^{2} (x) - 2 (x ln (x) - x))

= [x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))]_{0}^{1}

Compute the boundaries:

- 6

= - 6

What is the integral from 0 to 1 of ln^3(x) ?
The integral from 0 to 1 of ln^3(x) is -6