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Popular Calculus >

integral of (b-x)/x

Solution

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

Solution

b ln ∣ x ∣ - x + C

Solution steps

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

Expand

\frac{b - x}{x} : \frac{b}{x} - 1

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

\int \frac{b}{x} d x = b ln ∣ x ∣

\int 1 d x = x

= b ln ∣ x ∣ - x

Add a constant to the solution

= b ln ∣ x ∣ - x + C

Graph

Popular Examples

(\partial)/(\partial x)((e^y)/(x+y^3))

integral of 1/(a-x)

integral of (x+2)sqrt(4x+x^2)

integral of 1/(n^3)

limit as x approaches infinity of 3+4/x

Frequently Asked Questions (FAQ)

What is the integral of (b-x)/x ?
The integral of (b-x)/x is bln|x|-x+C