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Popular >

integral of (x+2)/x

Solution

\int \frac{x + 2}{x} d x

Solution

x + 2 ln ∣ x ∣ + C

Solution steps

\int \frac{x + 2}{x} d x

Expand

\frac{x + 2}{x} : 1 + \frac{2}{x}

= \int 1 + \frac{2}{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{2}{x} d x

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= x + 2 ln ∣ x ∣

Add a constant to the solution

= x + 2 ln ∣ x ∣ + C

Popular Examples

limit as x approaches-1 of 2x^2-4

x \to - 1 lim (2 x^{2} - 4)

derivative of (1+6x/(9-4x))

\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

area y^2-2x=7,x-y=4 area

y^{2} - 2 x = 7, x - y = 4

derivative of x^5*e^x derivative of

x^{5} \cdot e^{x}

area y=|x-12|,y= x/3 area

y = ∣ x - 12 ∣, y = \frac{x}{3}

Frequently Asked Questions (FAQ)

What is the integral of (x+2)/x ?
The integral of (x+2)/x is x+2ln|x|+C