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

The integral from 1 to 5 of x^5ln(x) is -434+15625/6 ln(5)

Popular >

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

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

- 434 + \frac{15625}{6} ln (5)

Decimal

3757.24456 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

= [\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}]_{1}^{5}

Compute the boundaries:

- 434 + \frac{15625}{6} ln (5)

= - 434 + \frac{15625}{6} ln (5)

\int_{0}^{3} - 2 x 9 - x^{2} d x

\int_{- 1}^{\infty} \frac{1}{x} d x

\int_{0}^{4} (x^{3} + 2) d x

\int_{2}^{\infty} \frac{1}{y ^{2} - 1} d y

\int_{- 1}^{1} (sin (x))^{2} d x

What is the integral from 1 to 5 of x^5ln(x) ?
The integral from 1 to 5 of x^5ln(x) is -434+15625/6 ln(5)