What is the integral of arccot(16y) ?

The integral of arccot(16y) is yarccot(16y)+1/32 ln|256y^2+1|+C

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integral of arccot(16y)

\int arccot (16 y) d y

y arccot (16 y) + \frac{1}{32} ln 256 y^{2} + 1 + C

Solution steps

\int arccot (16 y) d y

Apply Integration By Parts

: y arccot (16 y) - \int - \frac{16 y}{256 y ^{2} + 1} d y

= y arccot (16 y) - \int - \frac{16 y}{256 y ^{2} + 1} d y

\int - \frac{16 y}{256 y ^{2} + 1} d y = - \frac{1}{32} ln 256 y^{2} + 1

= y arccot (16 y) - (- \frac{1}{32} ln 256 y^{2} + 1)

Simplify

= y arccot (16 y) + \frac{1}{32} ln 256 y^{2} + 1

Add a constant to the solution

= y arccot (16 y) + \frac{1}{32} ln 256 y^{2} + 1 + C

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What is the integral of arccot(16y) ?
The integral of arccot(16y) is yarccot(16y)+1/32 ln|256y^2+1|+C