What is the integral of x*arccot(x) ?

The integral of x*arccot(x) is 1/2 x^2arccot(x)+1/2 (-arctan(x)+x)+C

Popular >

integral of x*arccot(x)

\int x \cdot arccot (x) d x

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

Solution steps

\int x arccot (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{( x ^{5} - 1 )}{( x - 1 )} d x

\int \frac{2 x - 3}{x ^{2} - 8 x + 7} d x

\int t t - 6 d t

\int 9 x (6 - x) d x

\int \frac{x}{( x ^{2} + 9 )} d x

What is the integral of x*arccot(x) ?
The integral of x*arccot(x) is 1/2 x^2arccot(x)+1/2 (-arctan(x)+x)+C