What is the integral of arccsc(t/2) ?

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

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integral of arccsc(t/2)

\int arccsc (\frac{t}{2}) d t

t arccsc (\frac{t}{2}) + 2 ln (\frac{1}{2} t^{2} - 4 + t) + C

Solution steps

\int arccsc (\frac{t}{2}) d t

Apply Integration By Parts

= t arccsc (\frac{t}{2}) - \int - \frac{2 t}{t ^{2} t ^{2} - 4} d t

\int - \frac{2 t}{t ^{2} t ^{2} - 4} d t = - 2 ln (\frac{1}{2} t^{2} - 4 + t)

= t arccsc (\frac{t}{2}) - (- 2 ln (\frac{1}{2} t^{2} - 4 + t))

Simplify

= t arccsc (\frac{t}{2}) + 2 ln (\frac{1}{2} t^{2} - 4 + t)

Add a constant to the solution

= t arccsc (\frac{t}{2}) + 2 ln (\frac{1}{2} t^{2} - 4 + t) + C

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