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

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

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integral of t*ln(t)

\int t \cdot 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

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