What is the integral from 1 to 5 of x^4ln(5x) ?

The integral from 1 to 5 of x^4ln(5x) is -3124/25+6249/5 ln(5)

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integral from 1 to 5 of x^4ln(5x)

\int_{1}^{5} x^{4} ln (5 x) d x

- \frac{3124}{25} + \frac{6249}{5} ln (5)

Decimal

1886.51550 \dots

Solution steps

\int_{1}^{5} x^{4} ln (5 x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- \frac{3124}{25} + \frac{6249}{5} ln (5)

= - \frac{3124}{25} + \frac{6249}{5} ln (5)

y = x^{3 - 3 x + 1}

\int 4 x - y^{2} d y

\int_{1}^{3} \frac{1}{x ^{2}} d x

\int (\frac{1}{z} - \frac{x}{y ^{2}}) d y

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

What is the integral from 1 to 5 of x^4ln(5x) ?
The integral from 1 to 5 of x^4ln(5x) is -3124/25+6249/5 ln(5)