What is the integral of ((8*x+5))/((x^2+1)) ?

The integral of ((8*x+5))/((x^2+1)) is 4ln|x^2+1|+5arctan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((8*x+5))/((x^2+1))

\int \frac{( 8 \cdot x + 5 )}{( x ^{2} + 1 )} d x

4 ln x^{2} + 1 + 5 arctan (x) + C

Solution steps

\int \frac{8 x + 5}{x ^{2} + 1} d x

Expand

\frac{8 x + 5}{x ^{2} + 1} : \frac{8 x}{x ^{2} + 1} + \frac{5}{x ^{2} + 1}

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{8 x}{x ^{2} + 1} d x + \int \frac{5}{x ^{2} + 1} d x

\int \frac{8 x}{x ^{2} + 1} d x = 4 ln x^{2} + 1

\int \frac{5}{x ^{2} + 1} d x = 5 arctan (x)

= 4 ln x^{2} + 1 + 5 arctan (x)

Add a constant to the solution

= 4 ln x^{2} + 1 + 5 arctan (x) + C

\int csc^{4} (5 x) d x

\int 1 - x x^{2} d x

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

\int 7 cos (7 x) d x

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

What is the integral of ((8*x+5))/((x^2+1)) ?
The integral of ((8*x+5))/((x^2+1)) is 4ln|x^2+1|+5arctan(x)+C