What is the integral of tln(2t) ?

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

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integral of tln(2t)

\int t ln (2 t) d t

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

Solution steps

\int t ln (2 t) d t

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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