What is the integral of (1/((sqrt(x))^2)+1/x) ?

The integral of (1/((sqrt(x))^2)+1/x) is 2ln|x|+C

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integral of (1/((sqrt(x))^2)+1/x)

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

2 ln ∣ x ∣ + C

Solution steps

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

\int \frac{1}{( x ) ^{2}} d x = ln ∣ x ∣

\int \frac{1}{x} d x = ln ∣ x ∣

= ln ∣ x ∣ + ln ∣ x ∣

Simplify

= 2 ln ∣ x ∣

Add a constant to the solution

= 2 ln ∣ x ∣ + C

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What is the integral of (1/((sqrt(x))^2)+1/x) ?
The integral of (1/((sqrt(x))^2)+1/x) is 2ln|x|+C