What is the integral of-3/(2t) ?

The integral of-3/(2t) is -3/2 ln|t|+C

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integral of-3/(2t)

\int - \frac{3}{2 t} d t

- \frac{3}{2} ln ∣ t ∣ + C

Solution steps

\int - \frac{3}{2 t} d t

Take the constant out:

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

= - \frac{3}{2} \cdot \int \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= - \frac{3}{2} ln ∣ t ∣

Add a constant to the solution

= - \frac{3}{2} ln ∣ t ∣ + C