https://file.aiquickdraw.com/mathbot/file/1725524222240xqop4cdu.jpg

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

Learn how to solve the integral ∫(6e^(1/x)/x^2) dx using the substitution method. This problem covers key calculus concepts, including integration of exponential functions. Suitable for college-level students.

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