What is the integral of 5/u ?

The integral of 5/u is 5ln|u|+C

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integral of 5/u

\int \frac{5}{u} d u

5 ln ∣ u ∣ + C

Solution steps

\int \frac{5}{u} d u

Take the constant out:

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

= 5 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Add a constant to the solution

= 5 ln ∣ u ∣ + C

\int \frac{5 x}{2} d x

\int - 4 x^{- 3} d x

\int - 3 ln (- 2 x) d x

\int 6^{2} d x

cos (5 x)