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

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

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integral of ln(sqrt(t))

\int ln (t) d t

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

Solution steps

\int ln (t) d t

Apply Integration By Parts

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

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

\int \frac{1}{2} d t = \frac{1}{2} t

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

Simplify

ln (t) : \frac{1}{2} ln (t)

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

Add a constant to the solution

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

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