What is the integral of tln(t) ?

The integral of tln(t) is 1/2 t^2ln(t)-(t^2)/4+C

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integral of tln(t)

\int t ln (t) d t

\frac{1}{2} t^{2} ln (t) - \frac{t ^{2}}{4} + C

Solution steps

\int t ln (t) d t

Apply Integration By Parts

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

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

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

= \frac{1}{2} t^{2} ln (t) - \frac{t ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} t^{2} ln (t) - \frac{t ^{2}}{4} + C

\frac{\partial}{\partial x} (ln (x^{2} - y^{2}))

\int_{1}^{2} \frac{2 x + 1}{x ^{2} + x} d x

\int_{1}^{3} 4 x^{3} - 8 x + 1 d x

9 t sin (π t)

\frac{1}{( 1 - x ) ^{3}}

What is the integral of tln(t) ?
The integral of tln(t) is 1/2 t^2ln(t)-(t^2)/4+C