What is the integral of arccot(8y) ?

The integral of arccot(8y) is yarccot(8y)+1/16 ln|64y^2+1|+C

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integral of arccot(8y)

\int arccot (8 y) d y

y arccot (8 y) + \frac{1}{16} ln 64 y^{2} + 1 + C

Solution steps

\int arccot (8 y) d y

Apply Integration By Parts

: y arccot (8 y) - \int - \frac{8 y}{64 y ^{2} + 1} d y

= y arccot (8 y) - \int - \frac{8 y}{64 y ^{2} + 1} d y

\int - \frac{8 y}{64 y ^{2} + 1} d y = - \frac{1}{16} ln 64 y^{2} + 1

= y arccot (8 y) - (- \frac{1}{16} ln 64 y^{2} + 1)

Simplify

= y arccot (8 y) + \frac{1}{16} ln 64 y^{2} + 1

Add a constant to the solution

= y arccot (8 y) + \frac{1}{16} ln 64 y^{2} + 1 + C

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What is the integral of arccot(8y) ?
The integral of arccot(8y) is yarccot(8y)+1/16 ln|64y^2+1|+C