What is the integral of arccsc(1/x) ?

The integral of arccsc(1/x) is xarccsc(1/x)+sqrt(1-x^2)+C

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integral of arccsc(1/x)

\int arccsc (\frac{1}{x}) d x

x arccsc (\frac{1}{x}) + 1 - x^{2} + C

Solution steps

\int arccsc (\frac{1}{x}) d x

Apply Integration By Parts

: x arccsc (\frac{1}{x}) - \int \frac{x}{1 - x ^{2}} d x

= x arccsc (\frac{1}{x}) - \int \frac{x}{1 - x ^{2}} d x

\int \frac{x}{1 - x ^{2}} d x = - 1 - x^{2}

= x arccsc (\frac{1}{x}) - (- 1 - x^{2})

Simplify

= x arccsc (\frac{1}{x}) + 1 - x^{2}

Add a constant to the solution

= x arccsc (\frac{1}{x}) + 1 - x^{2} + C

x \to 20 lim (- 85)

\int x^{3} 16 + x^{2} d x

\frac{x}{1 - ln ( x - 8 )}

4 x (x^{2} - 9)

x \to 0 lim (\frac{8 x}{cot ( x )})

What is the integral of arccsc(1/x) ?
The integral of arccsc(1/x) is xarccsc(1/x)+sqrt(1-x^2)+C