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Popular Calculus >

integral of ((x+1))/x

Solution

\int \frac{( x + 1 )}{x} d x

Solution

x + ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x + ln ∣ x ∣

Add a constant to the solution

= x + ln ∣ x ∣ + C

Graph

Popular Examples

y^{^{'}} = x + y, y (0) = 7

derivative of 2x^{-2}

\frac{d}{d x} (2 x^{- 2})

y^{''}-8y^'+20y=0

y^{^{''}} - 8 y^{^{'}} + 20 y = 0

integral from 1 to sqrt(2 of)x5^{(x^2)}

\int_{1}^{2} x 5^{(x^{2})} d x

limit as x approaches 0 of (3x^2-2x)/x

x \to 0 lim (\frac{3 x ^{2} - 2 x}{x})

Frequently Asked Questions (FAQ)

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