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Popular >

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

Popular Examples

tangent of f(x)=ln(x^3),\at x=e^5 tangent of

f (x) = ln (x^{3}), at x = e^{5}

tangent of f(x)=(x^3+6x)^4,\at x=2 tangent of

f (x) = (x^{3} + 6 x)^{4}, at x = 2

integral from 0 to 2 of (2x)/((x^2+3)^3)

\int_{0}^{2} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

slope of x^2+x slope

x^{2} + x

derivative of sin((pix)/3)derivative of

sin (\frac{π x}{3})

Frequently Asked Questions (FAQ)

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