What is the integral of arccot(2y) ?

The integral of arccot(2y) is yarccot(2y)+1/4 ln|4y^2+1|+C

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integral of arccot(2y)

\int arccot (2 y) d y

y arccot (2 y) + \frac{1}{4} ln 4 y^{2} + 1 + C

Solution steps

\int arccot (2 y) d y

Apply Integration By Parts

: y arccot (2 y) - \int - \frac{2 y}{4 y ^{2} + 1} d y

= y arccot (2 y) - \int - \frac{2 y}{4 y ^{2} + 1} d y

\int - \frac{2 y}{4 y ^{2} + 1} d y = - \frac{1}{4} ln 4 y^{2} + 1

= y arccot (2 y) - (- \frac{1}{4} ln 4 y^{2} + 1)

Simplify

= y arccot (2 y) + \frac{1}{4} ln 4 y^{2} + 1

Add a constant to the solution

= y arccot (2 y) + \frac{1}{4} ln 4 y^{2} + 1 + C

y^{^{'}} = \frac{x y ^{3}}{16}

\int x^{2} (4 - 2 x^{2}) d x

f (x) = x (x^{3} - x)

\frac{d}{d x} (\frac{6 x - 3}{5 x + 8})

\int \frac{4 x - 11}{2 x ^{2} - 11 x + 15} d x

What is the integral of arccot(2y) ?
The integral of arccot(2y) is yarccot(2y)+1/4 ln|4y^2+1|+C