The integral you want to solve is:

$\int \left(-10e^x\right)dx$

Solution:

The integral of $e^x$ is itself $e^x$. So we just apply this rule and handle the constant $-10$.

$\int \left(-10e^x\right)dx = -10 \int e^x dx = -10e^x + C$

where $C$ is the constant of integration.

Final Answer:

$-10e^x + C$

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the integral of $e^{2x}$?
2. How do you find the derivative of $e^x$?
3. What is the integral of $\cos(x)$?
4. How do constants affect integrals in general?
5. Can you explain integration by parts?

Tip: When integrating exponential functions, always remember that the derivative and integral of $e^x$ are both $e^x$, making them very straightforward!