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Popular >

integral of x^{-1}

Solution

integral

x^{- 1}

Solution

ln ∣ x ∣ + C

Solution steps

\int x^{- 1} d x

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

Popular Examples

integral of 1/x sqrt((1-x)/(1+x))

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

integral of 9x^2arcsin(x)

\int 9 x^{2} arcsin (x) d x

integral of (arcsin(e^x))/(e^x)

\int \frac{arcsin ( e ^{x} )}{e ^{x}} d x

integral of (cos(t))/(sin(t)+cos(t))

\int \frac{cos ( t )}{sin ( t ) + cos ( t )} d t

integral of 1/(sin(2x)cos(x))

\int \frac{1}{sin ( 2 x ) cos ( x )} d x

Frequently Asked Questions (FAQ)

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