To evaluate the integral of \( e^{xy} \) with respect to \( x \), we treat \( y \) as a constant because we are integrating with respect to \( x \). The integral can be solved using the following steps:

Given:
\[ \int e^{xy} \, dx \]

1. Recognize that \( y \) is a constant with respect to \( x \).
2. Use the fact that the integral of \( e^{ax} \) with respect to \( x \) is \( \frac{1}{a}e^{ax} \) for any constant \( a \).

So,
\[ \int e^{xy} \, dx = \frac{1}{y} e^{xy} + C \]

where \( C \) is the constant of integration.

Thus, the solution is:
\[ \int e^{xy} \, dx = \frac{1}{y} e^{xy} + C \]

Would you like more details or have any questions about this problem?

Here are 5 numbered questions you might want to ask next:
1. How do you integrate functions involving products of variables, such as \( x \cdot e^{xy} \)?
2. Can you show me how to solve a definite integral involving \( e^{xy} \)?
3. How do you find the partial derivative of \( e^{xy} \) with respect to \( x \) or \( y \)?
4. What are some applications of integrating functions of the form \( e^{xy} \)?
5. How do you solve an integral involving \( e^{x^2} \)?

**Tip:** When integrating functions with a constant multiplier, remember to factor out the constant to simplify the integration process.

Learn how to evaluate the integral of e^(xy) with respect to x using step-by-step instructions. This problem involves integrating exponential functions where y is treated as a constant. Suitable for undergraduate students studying calculus.

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