What is the integral of arccot(6y) ?

The integral of arccot(6y) is yarccot(6y)+1/12 ln|36y^2+1|+C

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integral of arccot(6y)

\int arccot (6 y) d y

y arccot (6 y) + \frac{1}{12} ln 36 y^{2} + 1 + C

Solution steps

\int arccot (6 y) d y

Apply Integration By Parts

: y arccot (6 y) - \int - \frac{6 y}{36 y ^{2} + 1} d y

= y arccot (6 y) - \int - \frac{6 y}{36 y ^{2} + 1} d y

\int - \frac{6 y}{36 y ^{2} + 1} d y = - \frac{1}{12} ln 36 y^{2} + 1

= y arccot (6 y) - (- \frac{1}{12} ln 36 y^{2} + 1)

Simplify

= y arccot (6 y) + \frac{1}{12} ln 36 y^{2} + 1

Add a constant to the solution

= y arccot (6 y) + \frac{1}{12} ln 36 y^{2} + 1 + C

x \to 0 + lim (x^{t a n (x)})

\int ((ln (x))^{2}) d x

4 x^{2} tan (x)

\frac{\partial}{\partial x} (x e x p (x, y, z) (- x^{2} - y^{2} - z^{2}))

f (x) = - 4 sin (x), at x = π

What is the integral of arccot(6y) ?
The integral of arccot(6y) is yarccot(6y)+1/12 ln|36y^2+1|+C