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The given integral is:

\[
\int e^{20x} \, dx
\]

### Solution:

The integral of an exponential function \( e^{ax} \) is generally given by:

\[
\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C
\]

Here, \( a = 20 \), so the integral becomes:

\[
\int e^{20x} \, dx = \frac{1}{20} e^{20x} + C
\]

### Verification by Differentiation:

To verify, let's differentiate the result \( \frac{1}{20} e^{20x} + C \):

\[
\frac{d}{dx} \left( \frac{1}{20} e^{20x} \right) = \frac{1}{20} \cdot 20 e^{20x} = e^{20x}
\]

Since the differentiation brings us back to the original function, the solution is correct.

### Final Answer:

\[
\int e^{20x} \, dx = \frac{1}{20} e^{20x} + C
\]

Would you like further details or explanations? Here are some related questions for practice:

1. What is the integral of \( e^{5x} \, dx \)?
2. How do you integrate \( e^{-3x} \, dx \)?
3. What is the general formula for integrating \( e^{ax + b} \, dx \)?
4. How would you solve \( \int e^{2x^2} \, dx \)?
5. Can you integrate \( e^{\sin x} \, dx \)?

**Tip:** When integrating exponential functions with coefficients in the exponent, always divide by that coefficient to adjust for the chain rule!

Find the integral given below: ∫e^(20x) dx.

Learn how to solve the integral of e^(20x) step-by-step using basic rules of calculus. This problem is suitable for students in Grades 11-12 and covers exponential function integration.

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