What is the integral from 1 to 3 of x^2ln(x) ?

The integral from 1 to 3 of x^2ln(x) is 9ln(3)-26/9

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integral from 1 to 3 of x^2ln(x)

\int_{1}^{3} x^{2} ln (x) d x

9 ln (3) - \frac{26}{9}

Decimal Notation

6.99862 \dots

Solution steps

\int_{1}^{3} 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}^{3}

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

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

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

Compute the boundaries:

9 ln (3) - \frac{26}{9}

= 9 ln (3) - \frac{26}{9}

\int \frac{5 x ^{2} + 2 x - 5}{x ^{3} - x} d x

f (x) = lo g_{10} (1 + x^{2})

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (3 x)

\frac{\partial}{\partial x} (6 y - 5 x^{2} e^{5 y})

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What is the integral from 1 to 3 of x^2ln(x) ?
The integral from 1 to 3 of x^2ln(x) is 9ln(3)-26/9