What is the integral of ((1-sqrt(x))^2)/x ?

The integral of ((1-sqrt(x))^2)/x is x-4sqrt(x)+ln|x|+1+C

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integral of ((1-sqrt(x))^2)/x

\int \frac{( 1 - x ) ^{2}}{x} d x

x - 4 x + ln ∣ x ∣ + 1 + C

Solution steps

\int \frac{( 1 - x ) ^{2}}{x} d x

Apply Integration By Parts

: (1 - x)^{2} - \int \frac{x - 1}{x} d x

= (1 - x)^{2} - \int \frac{x - 1}{x} d x

\int \frac{x - 1}{x} d x = 2 x - ln ∣ x ∣

= (1 - x)^{2} - (2 x - ln ∣ x ∣)

Simplify

(1 - x)^{2} - (2 x - ln ∣ x ∣) : x - 4 x + ln ∣ x ∣ + 1

= x - 4 x + ln ∣ x ∣ + 1

Add a constant to the solution

= x - 4 x + ln ∣ x ∣ + 1 + C

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What is the integral of ((1-sqrt(x))^2)/x ?
The integral of ((1-sqrt(x))^2)/x is x-4sqrt(x)+ln|x|+1+C