What is the integral of ((y+4))/(y^2+16) ?

The integral of ((y+4))/(y^2+16) is 1/2 ln|y^2+16|+arctan(y/4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((y+4))/(y^2+16)

\int \frac{( y + 4 )}{y ^{2} + 16} d y

\frac{1}{2} ln y^{2} + 16 + arctan (\frac{y}{4}) + C

Solution steps

\int \frac{y + 4}{y ^{2} + 16} d y

Expand

\frac{y + 4}{y ^{2} + 16} : \frac{y}{y ^{2} + 16} + \frac{4}{y ^{2} + 16}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{y}{y ^{2} + 16} d y + \int \frac{4}{y ^{2} + 16} d y

\int \frac{y}{y ^{2} + 16} d y = \frac{1}{2} ln y^{2} + 16

\int \frac{4}{y ^{2} + 16} d y = arctan (\frac{y}{4})

= \frac{1}{2} ln y^{2} + 16 + arctan (\frac{y}{4})

Add a constant to the solution

= \frac{1}{2} ln y^{2} + 16 + arctan (\frac{y}{4}) + C

\int \frac{x + 1}{4 + x ^{2}} d x

\int \frac{1}{ln ( x + 2 )} d x

\int x^{7} 1 + x^{4} d x

\int e^{4 x} tan (2 e^{4 x} + 3) d x

What is the integral of ((y+4))/(y^2+16) ?
The integral of ((y+4))/(y^2+16) is 1/2 ln|y^2+16|+arctan(y/4)+C