What is the integral of arctan(y) ?

The integral of arctan(y) is yarctan(y)-1/2 ln|y^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 arctan(y)

\int arctan (y) d y

y arctan (y) - \frac{1}{2} ln y^{2} + 1 + C

Solution steps

\int arctan (y) d y

Apply Integration By Parts

: y arctan (y) - \int \frac{y}{y ^{2} + 1} d y

= y arctan (y) - \int \frac{y}{y ^{2} + 1} d y

\int \frac{y}{y ^{2} + 1} d y = \frac{1}{2} ln y^{2} + 1

= y arctan (y) - \frac{1}{2} ln y^{2} + 1

Add a constant to the solution

= y arctan (y) - \frac{1}{2} ln y^{2} + 1 + C

f (x) = \frac{1}{2 x}

x \to 2 lim ((x + 1) (3 x^{2} - 9))

2 x^{2} + 5, [- 2, 3]

x \to 1 lim (\frac{∣ 1 - x ∣}{1 - x})

y^{^{''}} + y = 7 sin (x)

What is the integral of arctan(y) ?
The integral of arctan(y) is yarctan(y)-1/2 ln|y^2+1|+C