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

The integral of (9/x+x/9) is 9ln|x|+(x^2)/(18)+C

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integral of (9/x+x/9)

\int (\frac{9}{x} + \frac{x}{9}) d x

9 ln ∣ x ∣ + \frac{x ^{2}}{18} + C

Solution steps

\int \frac{9}{x} + \frac{x}{9} d x

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{9}{x} d x + \int \frac{x}{9} d x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

\int \frac{x}{9} d x = \frac{x ^{2}}{18}

= 9 ln ∣ x ∣ + \frac{x ^{2}}{18}

Add a constant to the solution

= 9 ln ∣ x ∣ + \frac{x ^{2}}{18} + C

y = - 2 x + 2

\int (- 20 x^{3} - 6 x^{- 3}) d x

\frac{\partial}{\partial x} (\frac{7 y - 7 x}{y ^{2} + 2 x ^{2}})

(x^{2} - 2 x - 2 sin (x - 2))^{^{'}}

x \to 2 lim (4 ln (2))

What is the integral of (9/x+x/9) ?
The integral of (9/x+x/9) is 9ln|x|+(x^2)/(18)+C