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Popular Calculus >

integral of (4x+1)/x

Solution

\int \frac{4 x + 1}{x} d x

Solution

4 x + ln ∣ x ∣ + C

Solution steps

\int \frac{4 x + 1}{x} d x

Expand

\frac{4 x + 1}{x} : 4 + \frac{1}{x}

= \int 4 + \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 4 d x + \int \frac{1}{x} d x

\int 4 d x = 4 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 4 x + ln ∣ x ∣

Add a constant to the solution

= 4 x + ln ∣ x ∣ + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (4x+1)/x ?
The integral of (4x+1)/x is 4x+ln|x|+C