What is the integral of arccot(13y) ?

The integral of arccot(13y) is yarccot(13y)+1/26 ln|169y^2+1|+C

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integral of arccot(13y)

\int arccot (13 y) d y

y arccot (13 y) + \frac{1}{26} ln 169 y^{2} + 1 + C

Solution steps

\int arccot (13 y) d y

Apply Integration By Parts

: y arccot (13 y) - \int - \frac{13 y}{169 y ^{2} + 1} d y

= y arccot (13 y) - \int - \frac{13 y}{169 y ^{2} + 1} d y

\int - \frac{13 y}{169 y ^{2} + 1} d y = - \frac{1}{26} ln 169 y^{2} + 1

= y arccot (13 y) - (- \frac{1}{26} ln 169 y^{2} + 1)

Simplify

= y arccot (13 y) + \frac{1}{26} ln 169 y^{2} + 1

Add a constant to the solution

= y arccot (13 y) + \frac{1}{26} ln 169 y^{2} + 1 + C

\int 1 + cos (8 x) d x

\frac{d}{d x} (cos (arctan (5 x)))

n = 0 \sum \infty n^{n} (x - 3)^{n}

x \to 2 lim (\frac{3}{x + 2})

\frac{s}{( s - 2 ) ( s - 3 ) ( s - 6 )}

What is the integral of arccot(13y) ?
The integral of arccot(13y) is yarccot(13y)+1/26 ln|169y^2+1|+C