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

The integral of ((1-sqrt(x))^2)/(x^2) is ((1-sqrt(x))^2)/x+ln|x|+6/(sqrt(x))-2/x+C

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

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

\frac{( 1 - x ) ^{2}}{x} + ln ∣ x ∣ + \frac{6}{x} - \frac{2}{x} + C

Solution steps

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

Apply Integration By Parts

: \frac{( 1 - x ) ^{2}}{x} - \int \frac{- x ^{\frac{3}{2}} ( - x + 1 ) - 2 x ( - x + 1 ) ^{2}}{x ^{3}} d x

= \frac{( 1 - x ) ^{2}}{x} - \int \frac{- x ^{\frac{3}{2}} ( - x + 1 ) - 2 x ( - x + 1 ) ^{2}}{x ^{3}} d x

\int \frac{- x ^{\frac{3}{2}} ( - x + 1 ) - 2 x ( - x + 1 ) ^{2}}{x ^{3}} d x = - ln ∣ x ∣ - \frac{6}{x} + \frac{2}{x}

= \frac{( 1 - x ) ^{2}}{x} - (- ln ∣ x ∣ - \frac{6}{x} + \frac{2}{x})

Simplify

= \frac{( 1 - x ) ^{2}}{x} + ln ∣ x ∣ + \frac{6}{x} - \frac{2}{x}

Add a constant to the solution

= \frac{( 1 - x ) ^{2}}{x} + ln ∣ x ∣ + \frac{6}{x} - \frac{2}{x} + C

\frac{d}{d x} (\frac{1}{2} ln^{2} (x))

- 7 csc (5 x) e^{3 x}

\int_{- 2}^{2 x} (3 t^{2} + 2 t) d t

\int_{0}^{4} x^{2} - 9 d x

\frac{3}{2 s + 1}

What is the integral of ((1-sqrt(x))^2)/(x^2) ?
The integral of ((1-sqrt(x))^2)/(x^2) is ((1-sqrt(x))^2)/x+ln|x|+6/(sqrt(x))-2/x+C