What is the integral of arccot(9y) ?

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

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integral of arccot(9y)

\int arccot (9 y) d y

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

Solution steps

\int arccot (9 y) d y

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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