What is the integral of xcot(x)csc(x) ?

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

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integral of xcot(x)csc(x)

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

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

Solution steps

\int x cot (x) csc (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

\frac{d}{d x} (ln (\frac{x ^{2} + 1}{x}))

\frac{\partial}{\partial x} (750 + 6 x - 7 y)

x^{2} - 3 x + 3, y = x

\int \frac{( ln ( x ) ) ^{44}}{x} d x

\int_{1}^{4} (x - 1) - (x^{2} - 4 x + 3) d x

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