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Popular Calculus >

integral of x/(x)

Solution

\int \frac{x}{d + x} d x

Solution

- d ln ∣ d + x ∣ + x + C

Solution steps

\int \frac{x}{d + x} d x

\frac{x}{d + x} = - \frac{d}{d + x} + 1

= \int - \frac{d}{d + x} + 1 d x

Apply the Sum Rule:

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

= - \int \frac{d}{d + x} d x + \int 1 d x

\int \frac{d}{d + x} d x = d ln ∣ d + x ∣

\int 1 d x = x

= - d ln ∣ d + x ∣ + x

Add a constant to the solution

= - d ln ∣ d + x ∣ + x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x/(x) ?
The integral of x/(x) is -dln|d+x|+x+C