What is the integral of 2 1/x ?

The integral of 2 1/x is 2ln|x|+C

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integral of 2 1/x

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

2 ln ∣ x ∣ + C

Solution steps

\int 2 \cdot \frac{1}{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

\int e^{- 7 x} tan (e^{- 7 x}) d x

x y^{^{'}} + 2 y ln (x) = 3

\int_{1}^{3} \frac{x ^{2} + 8}{4 x - x ^{2}} d x

y^{^{'}} = x y

y = ln (x + x^{2} - 1)