What is the integral from 1 to 6 of sqrt(t)ln(t) ?

The integral from 1 to 6 of sqrt(t)ln(t) is 4sqrt(6)ln(6)-(8sqrt(2))/(sqrt(3))+4/9

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integral from 1 to 6 of sqrt(t)ln(t)

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

46 ln (6) - \frac{8 2}{3} + \frac{4}{9}

Decimal Notation

11.46805 \dots

Solution steps

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

Apply Integration By Parts

: [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \int \frac{2}{3} t^{\frac{1}{2}} d t]_{1}^{6}

= [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \int \frac{2}{3} t^{\frac{1}{2}} d t]_{1}^{6}

\int \frac{2}{3} t^{\frac{1}{2}} d t = \frac{4}{9} t^{\frac{3}{2}}

= [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}}]_{1}^{6}

Compute the boundaries:

46 ln (6) - \frac{8 2}{3} + \frac{4}{9}

= 46 ln (6) - \frac{8 2}{3} + \frac{4}{9}

\frac{d}{d x} (e^{-})

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

5 sin^{2} (x)

y = (6 x - 5)^{2} (3 - x^{5})^{2}

x \to - 1 lim (x^{3} + 1)

What is the integral from 1 to 6 of sqrt(t)ln(t) ?
The integral from 1 to 6 of sqrt(t)ln(t) is 4sqrt(6)ln(6)-(8sqrt(2))/(sqrt(3))+4/9