Integral of (-7x^9)dx dx

1. The integral of a constant times a function is the constant times the integral of the function:

   $$\int \left(\left(-7\right) x^{9} \cdot 1\right)\, dx = - 7 \int x^{9}\, dx$$

   1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$:

      $$\int x^{9}\, dx = \frac{x^{10}}{10}$$

   So, the result is: $- \frac{7 x^{10}}{10}$

2. Add the constant of integration:

   $$- \frac{7 x^{10}}{10}+ \mathrm{constant}$$

The answer is:

$$- \frac{7 x^{10}}{10}+ \mathrm{constant}$$