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Popular >

integral of 1/(x-9)

Solution

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

Solution

ln ∣ x - 9 ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 9

= ln ∣ x - 9 ∣

Add a constant to the solution

= ln ∣ x - 9 ∣ + C

Popular Examples

implicit y/(x-5y)=x^7+9 implicit derivative

\frac{y}{x - 5 y} = x^{7} + 9

xe^y(dy)/(dx)=2(e^y+x^3e^{2x})

x e^{y} \frac{d y}{d x} = 2 (e^{y} + x^{3} e^{2 x})

(dy)/(dx)=e^{5x}+10y

\frac{d y}{d x} = e^{5 x} + 10 y

integral from 0 to 1 of (1+e^x)/(e^x)

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x}} d x

(\partial)/(\partial x)((-x-6y)/(y^2+5x^2))

\frac{\partial}{\partial x} (\frac{- x - 6 y}{y ^{2} + 5 x ^{2}})

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-9) ?
The integral of 1/(x-9) is ln|x-9|+C