What is the integral of tcsc^2(t) ?

The integral of tcsc^2(t) is -tcot(t)+ln|sin(t)|+C

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integral of tcsc^2(t)

\int t csc^{2} (t) d t

- t cot (t) + ln ∣ sin (t) ∣ + C

Solution steps

\int t csc^{2} (t) d t

Apply Integration By Parts

= - t cot (t) - \int - cot (t) d t

\int - cot (t) d t = - ln ∣ sin (t) ∣

= - t cot (t) - (- ln ∣ sin (t) ∣)

Simplify

= - t cot (t) + ln ∣ sin (t) ∣

Add a constant to the solution

= - t cot (t) + ln ∣ sin (t) ∣ + C

What is the integral of tcsc^2(t) ?
The integral of tcsc^2(t) is -tcot(t)+ln|sin(t)|+C