What is the integral of (arccot(sqrt(t)))/(sqrt(t)) ?

The integral of (arccot(sqrt(t)))/(sqrt(t)) is 2sqrt(t)arccot(sqrt(t))+ln|t+1|+C

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integral of (arccot(sqrt(t)))/(sqrt(t))

\int \frac{arccot ( t )}{t} d t

2 t arccot (t) + ln ∣ t + 1 ∣ + C

Solution steps

\int \frac{arccot ( t )}{t} d t

Apply Integration By Parts

: 2 t arccot (t) - \int - \frac{1}{t + 1} d t

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

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

= 2 t arccot (t) - (- ln ∣ t + 1 ∣)

Simplify

= 2 t arccot (t) + ln ∣ t + 1 ∣

Add a constant to the solution

= 2 t arccot (t) + ln ∣ t + 1 ∣ + C

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