What is the integral of (2/x) ?

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

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integral of (2/x)

\int (\frac{2}{x}) d x

2 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 ln ∣ x ∣

Add a constant to the solution

= 2 ln ∣ x ∣ + C

f (x) = 6 x^{3} - 6 x^{2} + 4

x \to 0 + lim (2 x^{s i n (3 x)})

\int x e^{5 x + π} d x

x \to - 8 lim (- \frac{3 x}{x + 8})

3 x^{3} 25 - x^{2}