What is the integral of (1/(7x-2)-1/(7x+2)) ?

The integral of (1/(7x-2)-1/(7x+2)) is 1/7 ln|7x-2|-1/7 ln|7x+2|+C

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integral of (1/(7x-2)-1/(7x+2))

\int (\frac{1}{7 x - 2} - \frac{1}{7 x + 2}) d x

\frac{1}{7} ln ∣ 7 x - 2 ∣ - \frac{1}{7} ln ∣ 7 x + 2 ∣ + C

Solution steps

\int \frac{1}{7 x - 2} - \frac{1}{7 x + 2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{7 x - 2} d x - \int \frac{1}{7 x + 2} d x

\int \frac{1}{7 x - 2} d x = \frac{1}{7} ln ∣ 7 x - 2 ∣

\int \frac{1}{7 x + 2} d x = \frac{1}{7} ln ∣ 7 x + 2 ∣

= \frac{1}{7} ln ∣ 7 x - 2 ∣ - \frac{1}{7} ln ∣ 7 x + 2 ∣

Add a constant to the solution

= \frac{1}{7} ln ∣ 7 x - 2 ∣ - \frac{1}{7} ln ∣ 7 x + 2 ∣ + C

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What is the integral of (1/(7x-2)-1/(7x+2)) ?
The integral of (1/(7x-2)-1/(7x+2)) is 1/7 ln|7x-2|-1/7 ln|7x+2|+C