What is the integral of arccot(9x) ?

The integral of arccot(9x) is xarccot(9x)+1/18 ln|81x^2+1|+C

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integral of arccot(9x)

\int arccot (9 x) d x

x arccot (9 x) + \frac{1}{18} ln 81 x^{2} + 1 + C

Solution steps

\int arccot (9 x) d x

Apply Integration By Parts

: x arccot (9 x) - \int - \frac{9 x}{81 x ^{2} + 1} d x

= x arccot (9 x) - \int - \frac{9 x}{81 x ^{2} + 1} d x

\int - \frac{9 x}{81 x ^{2} + 1} d x = - \frac{1}{18} ln 81 x^{2} + 1

= x arccot (9 x) - (- \frac{1}{18} ln 81 x^{2} + 1)

Simplify

= x arccot (9 x) + \frac{1}{18} ln 81 x^{2} + 1

Add a constant to the solution

= x arccot (9 x) + \frac{1}{18} ln 81 x^{2} + 1 + C

y^{^{''}} - 2 y^{^{'}} - 15 y = 3 x cos (2 x)

x \to 2 lim (\frac{- 1 + x}{x - 2})

x \to \infty lim (- 2 e^{\frac{2}{x}})

9 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\int e^{4 x + 3} d x

What is the integral of arccot(9x) ?
The integral of arccot(9x) is xarccot(9x)+1/18 ln|81x^2+1|+C