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

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

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integral of 1/(7x)

\int \frac{1}{7 x} d x

\frac{1}{7} ln ∣ x ∣ + C

Solution steps

\int \frac{1}{7 x} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{7} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{7} ln ∣ x ∣ + C

\frac{d}{d x} ((- x^{2} - 3)^{2} x^{2} + 1)

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

\frac{d}{d x} (tan (11 x))

\int \frac{1}{∣ x ∣ x ^{2} - 1} d x

\int \frac{x}{x ^{2} + 1} - \frac{3}{3 x + 1} d x