What is the integral from 1 to 10 of x^2ln(x) ?

The integral from 1 to 10 of x^2ln(x) is -111+1000/3 ln(10)

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integral from 1 to 10 of x^2ln(x)

\int_{1}^{10} x^{2} ln (x) d x

- 111 + \frac{1000}{3} ln (10)

Decimal

656.52836 \dots

Solution steps

\int_{1}^{10} 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}^{10}

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{10}

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

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{10}

Compute the boundaries:

- 111 + \frac{1000}{3} ln (10)

= - 111 + \frac{1000}{3} ln (10)

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

\int_{0}^{1} \frac{8}{t ^{2} + 1} d t

\int_{5}^{x^{2}} \frac{1}{t ^{5}} d t

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

\int_{1}^{2} \frac{x}{( x ^{2} + 4 ) ^{3}} d x

What is the integral from 1 to 10 of x^2ln(x) ?
The integral from 1 to 10 of x^2ln(x) is -111+1000/3 ln(10)