What is the integral from 1 to 3 of x^4ln(x) ?

The integral from 1 to 3 of x^4ln(x) is -242/25+243/5 ln(3)

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integral from 1 to 3 of x^4ln(x)

\int_{1}^{3} x^{4} ln (x) d x

- \frac{242}{25} + \frac{243}{5} ln (3)

Decimal Notation

43.71255 \dots

Solution steps

\int_{1}^{3} x^{4} ln (x) d x

Apply Integration By Parts

: [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{3}

= [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{3}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{3}

Compute the boundaries:

- \frac{242}{25} + \frac{243}{5} ln (3)

= - \frac{242}{25} + \frac{243}{5} ln (3)

\frac{d y}{d t} = 5 y + y^{4}

\int \frac{x}{100} d x

\frac{\partial}{\partial x} (y - 4 x^{2} y^{- 2})

\frac{\partial ^{2}}{\partial x ^{2}} (ln (3 + x^{2} y^{2}))

(2 x y^{2} - 5) d x + (2 x^{2} y + 6) d y = 0

What is the integral from 1 to 3 of x^4ln(x) ?
The integral from 1 to 3 of x^4ln(x) is -242/25+243/5 ln(3)