What is the integral of u/v ?

The integral of u/v is uln|v|+C

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integral of u/v

\int \frac{u}{v} d v

u ln ∣ v ∣ + C

Solution steps

\int \frac{u}{v} d v

Take the constant out:

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

= u \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= u ln ∣ v ∣

Add a constant to the solution

= u ln ∣ v ∣ + C

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