What is the integral of 9/(x-4) ?

The integral of 9/(x-4) is 9ln|x-4|+C

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integral of 9/(x-4)

\int \frac{9}{x - 4} d x

9 ln ∣ x - 4 ∣ + C

Solution steps

\int \frac{9}{x - 4} d x

Take the constant out:

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

= 9 \cdot \int \frac{1}{x - 4} d x

Apply u-substitution

: \int \frac{1}{u} d u

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 ln ∣ u ∣

Substitute back

u = x - 4

= 9 ln ∣ x - 4 ∣

Add a constant to the solution

= 9 ln ∣ x - 4 ∣ + C

\frac{d}{d x} (tan (4 x^{5}))

\int_{0}^{1} \frac{1}{x - 2} d x

x \to 2 lim (x^{2} x)

f (x) = \frac{x}{( 5 x - 9 ) ^{5}}

\int \frac{x}{4 x ^{2} + 2 x + 5} d x