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Popular >

integral of (x+6)/x

Solution

\int \frac{x + 6}{x} d x

Solution

x + 6 ln ∣ x ∣ + C

Solution steps

\int \frac{x + 6}{x} d x

Expand

\frac{x + 6}{x} : 1 + \frac{6}{x}

= \int 1 + \frac{6}{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 1 d x + \int \frac{6}{x} d x

\int 1 d x = x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

= x + 6 ln ∣ x ∣

Add a constant to the solution

= x + 6 ln ∣ x ∣ + C

Graph

Popular Examples

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\int 6 x^{2} - 4 x + 5 d x

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\int (5 x^{4} + 6 x + \frac{1}{x ^{3}}) d x

Frequently Asked Questions (FAQ)

What is the integral of (x+6)/x ?
The integral of (x+6)/x is x+6ln|x|+C