What is the integral from 1 to 7 of x^2ln(x) ?

The integral from 1 to 7 of x^2ln(x) is -38+343/3 ln(7)

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integral from 1 to 7 of x^2ln(x)

\int_{1}^{7} x^{2} ln (x) d x

- 38 + \frac{343}{3} ln (7)

Decimal Notation

184.48239 \dots

Solution steps

\int_{1}^{7} 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}^{7}

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{7}

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

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{7}

Compute the boundaries:

- 38 + \frac{343}{3} ln (7)

= - 38 + \frac{343}{3} ln (7)

2 - x^{2}

\frac{d}{d t} (a cos (w (t) t) + b sin (w (t) t))

\frac{d}{d x} (ln (\frac{x ^{3}}{x ^{5} + 1}))

y = 10 + tan^{2} (x)

\int \frac{cot ( β )}{sin ^{6} ( β )} d β

What is the integral from 1 to 7 of x^2ln(x) ?
The integral from 1 to 7 of x^2ln(x) is -38+343/3 ln(7)