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

= (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

\frac{d}{d l} (2 π \frac{l}{9.8})

\frac{d y}{d x} + \frac{y}{x ( x + 1 )} = x + 1

\frac{d}{d x} ((x^{2} + 3 x)^{2})

\frac{16 x ^{3}}{3} - 4 x^{2} + 6 x - 13

\int_{0}^{3} (3 x + 2) d x

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