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Popular >

integral of x/(x-13)

Solution

\int \frac{x}{x - 13} d x

Solution

x - 13 + 13 ln ∣ x - 13 ∣ + C

Solution steps

\int \frac{x}{x - 13} d x

Apply u-substitution

: \int \frac{u + 13}{u} d u

= \int \frac{u + 13}{u} d u

Expand

\frac{u + 13}{u} : 1 + \frac{13}{u}

= \int 1 + \frac{13}{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{13}{u} d u

\int 1 d u = u

\int \frac{13}{u} d u = 13 ln ∣ u ∣

= u + 13 ln ∣ u ∣

Substitute back

u = x - 13

= x - 13 + 13 ln ∣ x - 13 ∣

Add a constant to the solution

= x - 13 + 13 ln ∣ x - 13 ∣ + C

Graph

Popular Examples

integral of cos^4(3x)

\int cos^{4} (3 x) d x

y=(dy)/(dx)x-(dy)/(dx)^2

y = \frac{d y}{d x} x - \frac{d y}{d x}^{2}

area y=5x^2,y^2= 1/5 x area

y = 5 x^{2}, y^{2} = \frac{1}{5} x

\frac{d y}{d x} = x^{6} y

limit as x approaches 100 of 8x

x \to 100 lim (8 x)

Frequently Asked Questions (FAQ)

What is the integral of x/(x-13) ?
The integral of x/(x-13) is x-13+13ln|x-13|+C