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

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

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

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

t - 4 t + ln ∣ t ∣ + 1 + C

Solution steps

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

Apply Integration By Parts

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

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

= (1 - t)^{2} - (2 t - ln ∣ t ∣)

Simplify

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

= t - 4 t + ln ∣ t ∣ + 1

Add a constant to the solution

= t - 4 t + ln ∣ t ∣ + 1 + C

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