What is the integral of-ln(t) ?

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

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integral of-ln(t)

\int - ln (t) d t

- t ln (t) + t + C

Solution steps

\int - ln (t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln (t) d t

Apply Integration By Parts

= - (t ln (t) - \int 1 d t)

\int 1 d t = t

= - (t ln (t) - t)

Simplify

= - t ln (t) + t

Add a constant to the solution

= - t ln (t) + t + C