What is the integral from 1 to 6 of xln(x) ?

The integral from 1 to 6 of xln(x) is 18ln(6)-35/4

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integral from 1 to 6 of xln(x)

\int_{1}^{6} x ln (x) d x

18 ln (6) - \frac{35}{4}

Decimal

23.50167 \dots

Solution steps

\int_{1}^{6} x ln (x) d x

Apply Integration By Parts

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{6}

Compute the boundaries:

18 ln (6) - \frac{35}{4}

= 18 ln (6) - \frac{35}{4}

s l o p e in t erce pt (46, 381), (64, 444)

\frac{d}{d x} (\frac{6000}{x})

\int \frac{1}{2 sin ( x ) cos ( x )} d x

d er i v a t i v e 1500 x + 3000 (3 x + 3)^{- 1} - 1000

a re a x^{\frac{2}{7}}, 1, x = 0

What is the integral from 1 to 6 of xln(x) ?
The integral from 1 to 6 of xln(x) is 18ln(6)-35/4