What is the integral of tcsc(t)cot(t) ?

The integral of tcsc(t)cot(t) is -tcsc(t)+ln|tan(t/2)|+C

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integral of tcsc(t)cot(t)

\int t csc (t) cot (t) d t

- t csc (t) + ln tan (\frac{t}{2}) + C

Solution steps

\int t csc (t) cot (t) d t

Apply Integration By Parts

: - t csc (t) - \int - csc (t) d t

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

\int - csc (t) d t = - ln tan (\frac{t}{2})

= - t csc (t) - (- ln tan (\frac{t}{2}))

Simplify

= - t csc (t) + ln tan (\frac{t}{2})

Add a constant to the solution

= - t csc (t) + ln tan (\frac{t}{2}) + C

\frac{d}{d x} (\frac{5}{cos ^{2} ( x )})

x \to 2 - lim (\frac{7}{x - 2})

f (x) = 3 x^{2} + 3 x + 3

\int e^{x} (1 + e^{1 - x}) d x

x y^{^{'}} + 6 x^{2} y = x e^{5 x}

What is the integral of tcsc(t)cot(t) ?
The integral of tcsc(t)cot(t) is -tcsc(t)+ln|tan(t/2)|+C