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Popular Calculus >

integral of (x-1)/x

Solution

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

Solution

x - ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x - ln ∣ x ∣

Add a constant to the solution

= x - ln ∣ x ∣ + C

Graph

Popular Examples

derivative of sin((pix)/3)

d er i v a t i v e sin (\frac{π x}{3})

derivative of f(x)= 3/(2x-4)

d er i v a t i v e f (x) = \frac{3}{2 x - 4}

derivative of e^{2sin(3v)}

d er i v a t i v e e^{2 s i n (3 v)}

derivative of xy+ln(x/y)

\frac{d}{d x} (x y + ln (\frac{x}{y}))

y^{''}-6y^'+9y=0,y(0)=2,y^'(0)= 25/3

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{25}{3}

Frequently Asked Questions (FAQ)

What is the integral of (x-1)/x ?
The integral of (x-1)/x is x-ln|x|+C