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Popular >

integral of x/(x-9)

Solution

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

Solution

x - 9 + 9 ln ∣ x - 9 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{u + 9}{u} d u

= \int \frac{u + 9}{u} d u

Expand

\frac{u + 9}{u} : 1 + \frac{9}{u}

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

Apply the Sum Rule:

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

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

\int 1 d u = u

\int \frac{9}{u} d u = 9 ln ∣ u ∣

= u + 9 ln ∣ u ∣

Substitute back

u = x - 9

= x - 9 + 9 ln ∣ x - 9 ∣

Add a constant to the solution

= x - 9 + 9 ln ∣ x - 9 ∣ + C

Graph

Popular Examples

integral of 1/(xsqrt(x^3-1))

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

integral of (-3)/(x^2)+11-4^x

\int \frac{- 3}{x ^{2}} + 11 - 4^{x} d x

derivative of sin^5(x^3)derivative of

sin^{5} (x^{3})

limit as x approaches 5 of |x-5|

x \to 5 lim (∣ x - 5 ∣)

y^'-y/2 =e^{-t}

y^{^{'}} - \frac{y}{2} = e^{- t}

Frequently Asked Questions (FAQ)

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