What is the integral of sqrt(t)*ln(t) ?

The integral of sqrt(t)*ln(t) is 2/3 t^{3/2}ln(t)-4/9 t^{3/2}+C

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integral of sqrt(t)*ln(t)

\int t \cdot ln (t) d t

\frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}} + C

Solution steps

\int 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

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

\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}}

Add a constant to the solution

= \frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}} + C

y = (4 x^{2} + 5) (3 x - 5)

2 x^{3} - 3 x^{2} - 72 x + 2

\frac{s + 1}{s ^{2} - 4 s}

2 \cdot e^{x^{2} - 4 x}

\int 2 x - 5 d x

What is the integral of sqrt(t)*ln(t) ?
The integral of sqrt(t)*ln(t) is 2/3 t^{3/2}ln(t)-4/9 t^{3/2}+C