What is the integral of k/(x^n) ?

The integral of k/(x^n) is (kx^{-n+1})/(-n+1)+C

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integral of k/(x^n)

\int \frac{k}{x ^{n}} d x

\frac{k x ^{- n + 1}}{- n + 1} + C

Solution steps

\int \frac{k}{x ^{n}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= k \cdot \int \frac{1}{x ^{n}} d x

Apply the Power Rule

= k \frac{x ^{- n + 1}}{- n + 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{k x ^{- n + 1}}{- n + 1}

Add a constant to the solution

= \frac{k x ^{- n + 1}}{- n + 1} + C

What is the integral of k/(x^n) ?
The integral of k/(x^n) is (kx^{-n+1})/(-n+1)+C