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

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

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integral of ln(t^2)

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

2 t ln (t) - 2 t + C

Solution steps

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

Apply Integration By Parts

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

\int 2 d t = 2 t

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 2 t ln (t) - 2 t

Add a constant to the solution

= 2 t ln (t) - 2 t + C