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Popular >

integral of ((3+x))/x

Solution

\int \frac{( 3 + x )}{x} d x

Solution

3 ln ∣ x ∣ + x + C

Solution steps

\int \frac{3 + x}{x} d x

Expand

\frac{3 + x}{x} : \frac{3}{x} + 1

= \int \frac{3}{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{3}{x} d x + \int 1 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= 3 ln ∣ x ∣ + x

Add a constant to the solution

= 3 ln ∣ x ∣ + x + C

Graph

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integral of ((x-sqrt(x))/3)

\int (\frac{x - x}{3}) d x

Frequently Asked Questions (FAQ)

What is the integral of ((3+x))/x ?
The integral of ((3+x))/x is 3ln|x|+x+C