What is the integral of xarccot(x) ?

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

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integral of xarccot(x)

\int x 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

f^{^{''}} (x) = x^{- \frac{3}{2}}, f^{^{'}} (4) = 7, f (0) = 0

\frac{d}{d x} (\frac{2}{( x - 1 ) ^{3}})

\frac{2 \cdot ( s - 1 ) \cdot e ^{- 2 s}}{s ^{2} - 2 s + 2}

y = x^{2} + 2, (- 4, 18)

y = 7 x, y = \frac{7}{4} x, y = 78 - x^{2}

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