What is the integral of 8x^{-1} ?

The integral of 8x^{-1} is 8ln|x|+C

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integral of 8x^{-1}

\int 8 x^{- 1} d x

8 ln ∣ x ∣ + C

Solution steps

\int 8 x^{- 1} d x

Take the constant out:

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

= 8 \cdot \int x^{- 1} d x

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= 8 ln ∣ x ∣

Add a constant to the solution

= 8 ln ∣ x ∣ + C

\int \frac{1}{x ^{2} + 8} d x

f (x) = - 2 x^{3}

\frac{s - 1}{2 s ^{2} + s + 6}

\int_{2}^{4} (2 x^{2} - 3 x + 1) d x

x \to - 2 lim (\frac{3}{x + 2})