What is the integral of arccot(10y) ?

The integral of arccot(10y) is yarccot(10y)+1/20 ln|100y^2+1|+C

Popular >

integral of arccot(10y)

\int arccot (10 y) d y

y arccot (10 y) + \frac{1}{20} ln 100 y^{2} + 1 + C

Solution steps

\int arccot (10 y) d y

Apply Integration By Parts

: y arccot (10 y) - \int - \frac{10 y}{100 y ^{2} + 1} d y

= y arccot (10 y) - \int - \frac{10 y}{100 y ^{2} + 1} d y

\int - \frac{10 y}{100 y ^{2} + 1} d y = - \frac{1}{20} ln 100 y^{2} + 1

= y arccot (10 y) - (- \frac{1}{20} ln 100 y^{2} + 1)

Simplify

= y arccot (10 y) + \frac{1}{20} ln 100 y^{2} + 1

Add a constant to the solution

= y arccot (10 y) + \frac{1}{20} ln 100 y^{2} + 1 + C

\frac{d}{d x} (\frac{( x - 5 ) ( x ^{2} + 5 x + 25 )}{x ^{3}})

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

\int \frac{x + 2}{2 x + 1} d x

(\frac{x - 5}{x + 5})^{4}

10 y^{^{''}} + 1000 y = 50 cos (8 t)

What is the integral of arccot(10y) ?
The integral of arccot(10y) is yarccot(10y)+1/20 ln|100y^2+1|+C