What is the integral of ((x+6))/(x^2+9) ?

The integral of ((x+6))/(x^2+9) is 1/2 ln|x^2+9|+2arctan(x/3)+C

Popular >

integral of ((x+6))/(x^2+9)

\int \frac{( x + 6 )}{x ^{2} + 9} d x

\frac{1}{2} ln x^{2} + 9 + 2 arctan (\frac{x}{3}) + C

Solution steps

\int \frac{x + 6}{x ^{2} + 9} d x

Expand

\frac{x + 6}{x ^{2} + 9} : \frac{x}{x ^{2} + 9} + \frac{6}{x ^{2} + 9}

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{x}{x ^{2} + 9} d x + \int \frac{6}{x ^{2} + 9} d x

\int \frac{x}{x ^{2} + 9} d x = \frac{1}{2} ln x^{2} + 9

\int \frac{6}{x ^{2} + 9} d x = 2 arctan (\frac{x}{3})

= \frac{1}{2} ln x^{2} + 9 + 2 arctan (\frac{x}{3})

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 9 + 2 arctan (\frac{x}{3}) + C

\frac{s + 1}{s ^{2} - 3 s + 2}

\frac{\partial}{\partial x} (9 x + y + 7 x y)

f^{^{'}} (x) = 1 - 2 x

x \to \infty lim (x^{2} + 5 x)

\frac{d}{d x} (3 x + 6)

What is the integral of ((x+6))/(x^2+9) ?
The integral of ((x+6))/(x^2+9) is 1/2 ln|x^2+9|+2arctan(x/3)+C