What is the integral of ((10)/x+x/(10)) ?

The integral of ((10)/x+x/(10)) is 10ln|x|+(x^2)/(20)+C

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integral of ((10)/x+x/(10))

\int (\frac{10}{x} + \frac{x}{10}) d x

10 ln ∣ x ∣ + \frac{x ^{2}}{20} + C

Solution steps

\int \frac{10}{x} + \frac{x}{10} 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{10}{x} d x + \int \frac{x}{10} d x

\int \frac{10}{x} d x = 10 ln ∣ x ∣

\int \frac{x}{10} d x = \frac{x ^{2}}{20}

= 10 ln ∣ x ∣ + \frac{x ^{2}}{20}

Add a constant to the solution

= 10 ln ∣ x ∣ + \frac{x ^{2}}{20} + C

x \to \infty lim (x^{2} 9)

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What is the integral of ((10)/x+x/(10)) ?
The integral of ((10)/x+x/(10)) is 10ln|x|+(x^2)/(20)+C