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

The integral of (ln(t))/(sqrt(t)) is 2sqrt(t)ln(t)-4sqrt(t)+C

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integral of (ln(t))/(sqrt(t))

\int \frac{ln ( t )}{t} d t

2 t ln (t) - 4 t + C

Solution steps

\int \frac{ln ( t )}{t} d t

Apply Integration By Parts

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

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

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

= 2 t ln (t) - 4 t

Add a constant to the solution

= 2 t ln (t) - 4 t + C

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