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Popular >

integral of 1+1/x

Solution

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

Solution

x + ln ∣ x ∣ + C

Solution steps

\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

(\partial)/(\partial y)(sqrt(5x^2+8xy+y^2))

\frac{\partial}{\partial y} (5 x^{2} + 8 x y + y^{2})

(dy)/(dx)+(5x^2)/(e^{3x^3)}y=0

\frac{d y}{d x} + \frac{5 x ^{2}}{e ^{3 x^{3}}} y = 0

xy^'-2y=2x^2+x-2

x y^{^{'}} - 2 y = 2 x^{2} + x - 2

integral of ((x^2-x+4))/(x^3+2x)

\int \frac{( x ^{2} - x + 4 )}{x ^{3} + 2 x} d x

integral of ((1-2x)^2)/x

\int \frac{( 1 - 2 x ) ^{2}}{x} d x

Frequently Asked Questions (FAQ)

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