What is the integral of arccot(x) ?

The integral of arccot(x) is xarccot(x)+1/2 ln|x^2+1|+C

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integral of arccot(x)

\int arccot (x) d x

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

Solution steps

\int arccot (x) d x

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

y^{^{'}} + 2 y = t e^{- 2 t}

x^{2} y^{^{''}} + 2 x y^{^{'}} + 100.25 y = 0

f (x) = (ln (x))^{2}

y^{^{''}} - 4 y = e^{2 t}

\int_{\frac{1}{2}}^{3} 8 x ln (2 x) d x

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