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Popular >

integral of x/(x-14)

Solution

\int \frac{x}{x - 14} d x

Solution

x - 14 + 14 ln ∣ x - 14 ∣ + C

Solution steps

\int \frac{x}{x - 14} d x

Apply u-substitution

: \int \frac{u + 14}{u} d u

= \int \frac{u + 14}{u} d u

Expand

\frac{u + 14}{u} : 1 + \frac{14}{u}

= \int 1 + \frac{14}{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{14}{u} d u

\int 1 d u = u

\int \frac{14}{u} d u = 14 ln ∣ u ∣

= u + 14 ln ∣ u ∣

Substitute back

u = x - 14

= x - 14 + 14 ln ∣ x - 14 ∣

Add a constant to the solution

= x - 14 + 14 ln ∣ x - 14 ∣ + C

Popular Examples

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\int ln (x) \cdot x^{2} d x

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integral of (e^{-x})/(e^{-x)+e^x}

\int \frac{e ^{- x}}{e ^{- x} + e ^{x}} d x

integral of sqrt(x^2-2x-1)

\int x^{2} - 2 x - 1 d x

integral of (csc^2(sqrt(x)))/(sqrt(x))

\int \frac{csc ^{2} ( x )}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of x/(x-14) ?
The integral of x/(x-14) is x-14+14ln|x-14|+C