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

The integral from 1 to 5 of x^2ln(x) is -124/9+125/3 ln(5)

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

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

- \frac{124}{9} + \frac{125}{3} ln (5)

Decimal Notation

53.28213 \dots

Solution steps

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

Apply Integration By Parts

: [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{5}

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{5}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{5}

Compute the boundaries:

- \frac{124}{9} + \frac{125}{3} ln (5)

= - \frac{124}{9} + \frac{125}{3} ln (5)

\frac{d y}{d x} = \frac{1}{5} (8 - y)

1 - \frac{1}{1 + x}

\frac{d}{d x} (4 x^{2} 5 x + 1)

\int \frac{5}{4 sin ( x ) + 3 cos ( x )} d x

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0, y (1) = 0, y^{^{'}} (1) = - 4

What is the integral from 1 to 5 of x^2ln(x) ?
The integral from 1 to 5 of x^2ln(x) is -124/9+125/3 ln(5)