What is the integral of arccot(3x) ?

The integral of arccot(3x) is xarccot(3x)+1/6 ln|9x^2+1|+C

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integral of arccot(3x)

\int arccot (3 x) d x

x arccot (3 x) + \frac{1}{6} ln 9 x^{2} + 1 + C

Solution steps

\int arccot (3 x) d x

Apply Integration By Parts

: x arccot (3 x) - \int - \frac{3 x}{9 x ^{2} + 1} d x

= x arccot (3 x) - \int - \frac{3 x}{9 x ^{2} + 1} d x

\int - \frac{3 x}{9 x ^{2} + 1} d x = - \frac{1}{6} ln 9 x^{2} + 1

= x arccot (3 x) - (- \frac{1}{6} ln 9 x^{2} + 1)

Simplify

= x arccot (3 x) + \frac{1}{6} ln 9 x^{2} + 1

Add a constant to the solution

= x arccot (3 x) + \frac{1}{6} ln 9 x^{2} + 1 + C

y^{^{''}} - 2 y^{^{'}} + y = 12 e^{3 t}

y^{^{'}} + y = 6

y = \frac{x}{x + 3}, (1, 2)

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

\frac{6}{x}

What is the integral of arccot(3x) ?
The integral of arccot(3x) is xarccot(3x)+1/6 ln|9x^2+1|+C