What is the integral of arccot(3y) ?

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

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integral of arccot(3y)

\int arccot (3 y) d y

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

Solution steps

\int arccot (3 y) d y

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int x^{3} x d x

\int_{0}^{1} \frac{12}{4 x ^{2} + 5 x + 1} d x

x \to 2 lim (x (x - 4))

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

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