What is the integral of arccot(5y) ?

The integral of arccot(5y) is yarccot(5y)+1/10 ln|25y^2+1|+C

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integral of arccot(5y)

\int arccot (5 y) d y

y arccot (5 y) + \frac{1}{10} ln 25 y^{2} + 1 + C

Solution steps

\int arccot (5 y) d y

Apply Integration By Parts

: y arccot (5 y) - \int - \frac{5 y}{25 y ^{2} + 1} d y

= y arccot (5 y) - \int - \frac{5 y}{25 y ^{2} + 1} d y

\int - \frac{5 y}{25 y ^{2} + 1} d y = - \frac{1}{10} ln 25 y^{2} + 1

= y arccot (5 y) - (- \frac{1}{10} ln 25 y^{2} + 1)

Simplify

= y arccot (5 y) + \frac{1}{10} ln 25 y^{2} + 1

Add a constant to the solution

= y arccot (5 y) + \frac{1}{10} ln 25 y^{2} + 1 + C

f (x) = x^{2} - 6, (4, 10)

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

f (x) = \frac{1}{2 x}, at x = 81

\frac{d}{d x} (f (x) (\frac{x ^{4}}{4} - \frac{1}{4}))

lo g_{3} (x - 4 x^{2})

What is the integral of arccot(5y) ?
The integral of arccot(5y) is yarccot(5y)+1/10 ln|25y^2+1|+C