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Popular Calculus >

integral of (1+3x)/x

Solution

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

Solution

ln ∣ x ∣ + 3 x + C

Solution steps

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

Expand

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 3 d x = 3 x

= ln ∣ x ∣ + 3 x

Add a constant to the solution

= ln ∣ x ∣ + 3 x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (1+3x)/x ?
The integral of (1+3x)/x is ln|x|+3x+C