`int(1)/((7x-2)^(2))dx`

Answer

To solve the integral \( \int \frac{1}{(7x - 2)^2} \, dx \), we can use a standard integration formula. Here’s the step-by-step solution:

### Step 1: Identify the integral
We start with the integral:
\[ I = \int \frac{1}{(7x - 2)^2} \, dx \]

### Step 2: Use the integration formula
We can use the formula for integrating \( \frac{1}{(ax + b)^n} \):
\[ \int \frac{1}{(ax + b)^n} \, dx = \frac{1}{(n-1)a} \cdot \frac{1}{(ax + b)^{n-1}} + C \]
In our case, \( a = 7 \), \( b = -2 \), and \( n = 2 \).

### Step 3: Apply the formula
Substituting the values into the formula:
\[ I = \frac{1}{(2-1) \cdot 7} \cdot \frac{1}{(7x - 2)^{2-1}} + C \]
This simplifies to:
\[ I = \frac{1}{7} \cdot \frac{1}{(7x - 2)} + C \]

### Step 4: Simplify the result
Thus, we can write the result as:
\[ I = \frac{1}{7(7x - 2)} + C \]

### Final Answer
The final answer for the integral is:
\[ \int \frac{1}{(7x - 2)^2} \, dx = -\frac{1}{7(7x - 2)} + C \]