What is the integral of arccot(11y) ?

The integral of arccot(11y) is yarccot(11y)+1/22 ln|121y^2+1|+C

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integral of arccot(11y)

\int arccot (11 y) d y

y arccot (11 y) + \frac{1}{22} ln 121 y^{2} + 1 + C

Solution steps

\int arccot (11 y) d y

Apply Integration By Parts

: y arccot (11 y) - \int - \frac{11 y}{121 y ^{2} + 1} d y

= y arccot (11 y) - \int - \frac{11 y}{121 y ^{2} + 1} d y

\int - \frac{11 y}{121 y ^{2} + 1} d y = - \frac{1}{22} ln 121 y^{2} + 1

= y arccot (11 y) - (- \frac{1}{22} ln 121 y^{2} + 1)

Simplify

= y arccot (11 y) + \frac{1}{22} ln 121 y^{2} + 1

Add a constant to the solution

= y arccot (11 y) + \frac{1}{22} ln 121 y^{2} + 1 + C

f (x) = arctan (2 x)

\frac{d}{d x} ((x + 4) (e^{2} x))

f (x) = \frac{2 x}{x ^{2} + 1}, at x = 1

\int 2 x (x^{2} + 5)^{3} d x

x \to - 1 lim (\frac{6 x + 5}{5 x - 6})

What is the integral of arccot(11y) ?
The integral of arccot(11y) is yarccot(11y)+1/22 ln|121y^2+1|+C