What is the integral from 0 to 1 of x^5ln(x) ?

The integral from 0 to 1 of x^5ln(x) is -1/36

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integral from 0 to 1 of x^5ln(x)

\int_{0}^{1} x^{5} ln (x) d x

- \frac{1}{36}

Decimal Notation

- 0.02777 \dots

Solution steps

\int_{0}^{1} x^{5} ln (x) d x

Apply Integration By Parts

: [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{0}^{1}

= [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{0}^{1}

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= [\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}]_{0}^{1}

Compute the boundaries:

- \frac{1}{36}

= - \frac{1}{36}

\frac{d}{d x} (3 arctan (2 x))

\int (\frac{z ^{4} + 10 z ^{3}}{2 z ^{2}}) d z

y^{^{'}} - \frac{2 y}{x} = x^{2} e^{x}

\frac{\partial}{\partial x} (e^{- k x^{2}})

\frac{d y}{d x} = y (x^{2} + 2)

What is the integral from 0 to 1 of x^5ln(x) ?
The integral from 0 to 1 of x^5ln(x) is -1/36