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

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

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integral of ((11+x))/x

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

11 ln ∣ x ∣ + x + C

Solution steps

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

Expand

\frac{11 + x}{x} : \frac{11}{x} + 1

= \int \frac{11}{x} + 1 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 1 d x

\int \frac{11}{x} d x = 11 ln ∣ x ∣

\int 1 d x = x

= 11 ln ∣ x ∣ + x

Add a constant to the solution

= 11 ln ∣ x ∣ + x + C

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