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Popular >

integral of r^{-1}

Solution

\int r^{- 1} d r

Solution

ln ∣ r ∣ + C

Solution steps

\int r^{- 1} d r

Use the common integral:

\int r^{- 1} d r = ln (∣ r ∣)

= ln ∣ r ∣

Add a constant to the solution

= ln ∣ r ∣ + C

Graph

Popular Examples

integral of 7x^2+8x^{-2}

\int 7 x^{2} + 8 x^{- 2} d x

integral of 5x(2x^2+1)^{-3}

\int 5 x (2 x^{2} + 1)^{- 3} d x

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

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

integral of ((3+r)/r)^2

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

integral of sqrt(1+((x^6-1)/(2x^3))^2)

\int 1 + (\frac{x ^{6} - 1}{2 x ^{3}})^{2} d x

Frequently Asked Questions (FAQ)

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