What is the integral of arccsc(x) ?

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

Popular >

integral of arccsc(x)

\int arccsc (x) d x

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

Solution steps

\int arccsc (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{x ^{n}}{n + 5}

\frac{\partial}{\partial x} (7 x y^{4} + 2)

\int \frac{1}{( x + 1 ) ( x ^{2} + 25 )} d x

\int (x^{\frac{3}{2}} + 8)^{6} x d x

n = 1 \sum \infty (- \frac{10}{11})^{n}

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