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Popular >

integral of (1-1/x)

Solution

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

Solution

x - ln ∣ x ∣ + C

Solution steps

\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

(\partial)/(\partial t)(e^{-2t})

\frac{\partial}{\partial t} (e^{- 2 t})

integral of x^4-6x

\int x^{4} - 6 x d x

derivative of 6e^xt+xt

\frac{d}{d x} (6 e^{x} t + x t)

area 7x,2x^2 area

7 x, 2 x^{2}

derivative of ln({f}(x)(x))

\frac{d}{d x} (ln (f (x)) (x))

Frequently Asked Questions (FAQ)

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