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Popular >

integral of x+x^{-1}

Solution

\int x + x^{- 1} d x

Solution

\frac{x ^{2}}{2} + ln ∣ x ∣ + C

Solution steps

\int x + x^{- 1} 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 x^{- 1} d x

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

\int x^{- 1} 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

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

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

integral of (z^3)/(\sqrt[3]{6+z^4)}

integral of 2x^2(x-2)

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

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

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

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

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

Frequently Asked Questions (FAQ)

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