What is the integral from 1 to 9 of sqrt(t)ln(t) ?

The integral from 1 to 9 of sqrt(t)ln(t) is 36ln(3)-104/9

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integral from 1 to 9 of sqrt(t)ln(t)

\int_{1}^{9} t ln (t) d t

36 ln (3) - \frac{104}{9}

Decimal Notation

27.99448 \dots

Solution steps

\int_{1}^{9} 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}^{9}

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

\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}^{9}

Compute the boundaries:

36 ln (3) - \frac{104}{9}

= 36 ln (3) - \frac{104}{9}

\frac{d}{d x} (\frac{cos ( x )}{1 + cot ( x )})

\int_{0}^{\frac{π}{4}} sin (3 x) d x

\frac{d}{d x} (\frac{2 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}})

\frac{d}{d x} (\frac{( x ^{2} - 2 x )}{x})

x \to 0 lim (\frac{tan ( 4 x )}{3 x})

What is the integral from 1 to 9 of sqrt(t)ln(t) ?
The integral from 1 to 9 of sqrt(t)ln(t) is 36ln(3)-104/9