What is the integral from 1 to 2 of x^5ln(x) ?

The integral from 1 to 2 of x^5ln(x) is -7/4+32/3 ln(2)

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integral from 1 to 2 of x^5ln(x)

\int_{1}^{2} x^{5} ln (x) d x

- \frac{7}{4} + \frac{32}{3} ln (2)

Decimal

5.64356 \dots

Solution steps

\int_{1}^{2} 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}^{2}

= [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{1}^{2}

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

= [\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}]_{1}^{2}

Compute the boundaries:

- \frac{7}{4} + \frac{32}{3} ln (2)

= - \frac{7}{4} + \frac{32}{3} ln (2)

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

y^{^{''}} - 2 y^{^{'}} = x + 2 e^{x}

\int (x^{2} - \frac{3}{x} + cos (x) - \frac{2}{x}) d x

y = x^{2} - 7

\frac{\partial}{\partial y} (x cos (y) - y cos (x))

What is the integral from 1 to 2 of x^5ln(x) ?
The integral from 1 to 2 of x^5ln(x) is -7/4+32/3 ln(2)