What is the integral of xcsc(x)cot(x) ?

The integral of xcsc(x)cot(x) is -xcsc(x)+ln|tan(x/2)|+C

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integral of xcsc(x)cot(x)

\int x csc (x) cot (x) d x

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

Solution steps

\int x csc (x) cot (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int_{0}^{8} x + 1 d x

\int sec (2 x + 1) tan (2 x + 1) d x

x \to 1 + lim (ln^{x - 1} (x))

\frac{d}{d t} (- cos^{2} (t))

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