What is the integral of 1/(9x) ?

The integral of 1/(9x) is 1/9 ln|x|+C

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integral of 1/(9x)

\int \frac{1}{9 x} d x

\frac{1}{9} ln ∣ x ∣ + C

Solution steps

\int \frac{1}{9 x} d x

Take the constant out:

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

= \frac{1}{9} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{9} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{9} ln ∣ x ∣ + C

\int \frac{x ^{2}}{x ^{2} - 4 x + 20} d x

7 e^{x}, 7 x e^{x^{2}}, 1, 7 e

f (x) = \frac{x}{( 1 + x ^{2} )}, at x = 2

\frac{d}{d x} (\frac{3}{x ^{6}} - \frac{1}{x ^{4}} + 5)

f (x) = (3 x^{2} + 2) (8 x^{3} - 3)