The integral in the image is:

$\int \frac{6e^{\frac{1}{x}}}{x^2} \, dx$

Let's solve this step by step. We can try substitution to handle the exponential term.

Step 1: Substitution

Let: $u = \frac{1}{x}$ Then, the derivative of $u$ is: $du = -\frac{1}{x^2} dx$

This substitution simplifies the integral:

$\int \frac{6e^{\frac{1}{x}}}{x^2} \, dx = 6 \int e^u (-du) = -6 \int e^u \, du$

Step 2: Integrate

The integral of $e^u$ is just $e^u$, so:

$-6 \int e^u \, du = -6e^u + C$

Step 3: Substitute back for $u$

Now, substitute $u = \frac{1}{x}$ back into the expression:

$-6e^{\frac{1}{x}} + C$

Final Answer:

The solution to the integral is:

$-6e^{\frac{1}{x}} + C$

Would you like any more details or further clarification on this solution?

5 Related Questions:

1. How do you handle integrals involving exponential functions with variable exponents?
2. Can you explain the method of substitution in integration?
3. What