What is the integral of tln(t^2) ?

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

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integral of tln(t^2)

\int t ln (t^{2}) d t

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

Solution steps

\int t ln (t^{2}) d t

Apply Integration By Parts

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

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

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

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

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

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

Add a constant to the solution

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

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