What is the integral of ((sqrt(x)-1)(sqrt(x)+1))/x ?

The integral of ((sqrt(x)-1)(sqrt(x)+1))/x is x-ln|x|+C

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integral of ((sqrt(x)-1)(sqrt(x)+1))/x

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

x - ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{( x - 1 ) ( 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

x \to π lim (15)

x \to 3 lim (5 x^{3} - 2 x^{2} + x - 7)

- 0.6 t^{3} + 7.2 t^{2} + 61

\frac{d}{d x} ((3 x - 5 y) e^{2 y - 4 x})

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