integral of 8x^{-9} — step-by-step solution

⚠ 8x is read as the product 8*x: for a power, write 8^x‖8x^{-9} is read as 8x^(-9)

Before performing the integration, let's calculate:

8 x^{-9}

\frac{8}{x^{9}}

Let's integrate:

\int(\frac{8}{x^{9}})dx

For the math expression:

\frac{8}{x^{9}}

, we know the derivative formula:

\frac{d}{d x} (a^{n}) = n a^{(n - 1)}

, so we try differentiating with ^(m+1)

Let's perform the differentiation:

\frac{d}{d x} (x^{(- 9 + 1)})

\frac{d}{d x} (x^{-8})

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{(n - 1)}

with f =

x

-8 x^{-9}

- \frac{8}{x^{9}}

The computed derivative matches the original math expression up to a constant factor. Therefore, the integral is:

\frac{8}{-8} \cdot \frac{1}{x^{8}}

- \frac{8}{8} \cdot \frac{1}{x^{8}}

ℹ

- \frac{8}{8}

-1

‖

-1 \cdot \frac{1}{x^{8}}

- \frac{1}{x^{8}}

- \frac{1}{x^{8}}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

- \frac{1}{x^{8}} + C