What is the integral of 5/x ?

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

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integral of 5/x

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

5 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 ln ∣ x ∣

Add a constant to the solution

= 5 ln ∣ x ∣ + C

g (x) = 6 x + 8

\int 2 x - y d x

x^{2} y^{^{'}} + y^{^{'}} = x y

y = x^{2} + 30 x + 225, y = 17 (x + 15)

\int \frac{5 x - 2}{x ^{2} + 6 x + 8} d x