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Popular >

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

Popular Examples

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

\frac{\partial}{\partial x} (\frac{e ^{y}}{x + y ^{3}})

limit as x approaches 0 of (x-20)/(x-4)

x \to 0 lim (\frac{x - 20}{x - 4})

(d^2y)/(dt^2)+2(dy)/(dt)+y=2

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + y = 2

integral of m 1 (v)(v)

\int m \frac{d}{1} (v) (v) d x

integral of 1/(a-x)

\int \frac{1}{a - x} d x

Frequently Asked Questions (FAQ)

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