What is the integral of ((11)/x+x/(11)) ?

The integral of ((11)/x+x/(11)) is 11ln|x|+(x^2)/(22)+C

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integral of ((11)/x+x/(11))

\int (\frac{11}{x} + \frac{x}{11}) d x

11 ln ∣ x ∣ + \frac{x ^{2}}{22} + C

Solution steps

\int \frac{11}{x} + \frac{x}{11} 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{11}{x} d x + \int \frac{x}{11} d x

\int \frac{11}{x} d x = 11 ln ∣ x ∣

\int \frac{x}{11} d x = \frac{x ^{2}}{22}

= 11 ln ∣ x ∣ + \frac{x ^{2}}{22}

Add a constant to the solution

= 11 ln ∣ x ∣ + \frac{x ^{2}}{22} + C

What is the integral of ((11)/x+x/(11)) ?
The integral of ((11)/x+x/(11)) is 11ln|x|+(x^2)/(22)+C