What is the integral of arccot(15y) ?

The integral of arccot(15y) is yarccot(15y)+1/30 ln|225y^2+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of arccot(15y)

\int arccot (15 y) d y

y arccot (15 y) + \frac{1}{30} ln 225 y^{2} + 1 + C

Solution steps

\int arccot (15 y) d y

Apply Integration By Parts

: y arccot (15 y) - \int - \frac{15 y}{225 y ^{2} + 1} d y

= y arccot (15 y) - \int - \frac{15 y}{225 y ^{2} + 1} d y

\int - \frac{15 y}{225 y ^{2} + 1} d y = - \frac{1}{30} ln 225 y^{2} + 1

= y arccot (15 y) - (- \frac{1}{30} ln 225 y^{2} + 1)

Simplify

= y arccot (15 y) + \frac{1}{30} ln 225 y^{2} + 1

Add a constant to the solution

= y arccot (15 y) + \frac{1}{30} ln 225 y^{2} + 1 + C

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

\int_{0}^{1} π^{9}

\frac{d}{d x} ((3 x^{2} - x - 4) (- x^{2} + 2))

\frac{d}{d x} (cosh (8 x + 1))

h \to 0.001 lim (\frac{e ^{h} - 1}{h})

What is the integral of arccot(15y) ?
The integral of arccot(15y) is yarccot(15y)+1/30 ln|225y^2+1|+C