What is the integral of 2/(5x) ?

The integral of 2/(5x) is 2/5 ln|x|+C

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integral of 2/(5x)

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

\frac{2}{5} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

= \frac{2}{5} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{2}{5} ln ∣ x ∣

Add a constant to the solution

= \frac{2}{5} ln ∣ x ∣ + C

\int (sec (4 x) - cot (4 x)) d x

\frac{d}{d x} (sin (2 π x))

\frac{\partial}{\partial x} (x^{3} + y^{2})

x^{2} y^{^{''}} + 15 x y^{^{'}} + 49 y = 0

\frac{1}{s ^{2} + 10.1 s + 1}