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Popular >

integral of x-1/x

Solution

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

Solution

\frac{x ^{2}}{2} - ln ∣ x ∣ + C

Solution steps

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

\int x d x = \frac{x ^{2}}{2}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - ln ∣ x ∣ + C

Popular Examples

tangent of y=(e^{-x})/(x+1)tangent of

y = \frac{e ^{- x}}{x + 1}

integral of 1/(x^2+3x+1)

\int \frac{1}{x ^{2} + 3 x + 1} d x

f^'(x)= 2/(sqrt(x))

f^{^{'}} (x) = \frac{2}{x}

slope of-2x^5+10x^3 slope

- 2 x^{5} + 10 x^{3}

integral of (e^x)/(e^{2x)+4e^x+4}

\int \frac{e ^{x}}{e ^{2 x} + 4 e ^{x} + 4} d x

Frequently Asked Questions (FAQ)

What is the integral of x-1/x ?
The integral of x-1/x is (x^2)/2-ln|x|+C