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Popular >

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

Popular Examples

integral of 1/(sqrt(e^{2x)+1)}

\int \frac{1}{e ^{2 x} + 1} d x

y^{''}+2y^'+2y=sin(x),y(0)=1,y^'(0)=-1

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (x), y (0) = 1, y^{^{'}} (0) = - 1

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

derivative of (4x^2+2x+8/(sqrt(x)))

\frac{d}{d x} (\frac{4 x ^{2} + 2 x + 8}{x})

derivative of 2x^{-2}

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

Frequently Asked Questions (FAQ)

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