Evaluate : `int(dx)/(1-sin^2x)`

Answer

To evaluate the integral \( \int \frac{dx}{1 - \sin^2 x} \), we can follow these steps:

### Step 1: Rewrite the Denominator
We start with the integral:
\[ \int \frac{dx}{1 - \sin^2 x} \]
Using the Pythagorean identity, we know that:
\[ \cos^2 x + \sin^2 x = 1 \implies 1 - \sin^2 x = \cos^2 x \]
So we can rewrite the integral as:
\[ \int \frac{dx}{\cos^2 x} \]

### Step 2: Simplify the Integral
The expression \( \frac{1}{\cos^2 x} \) can be rewritten using the secant function:
\[ \frac{1}{\cos^2 x} = \sec^2 x \]
Thus, our integral now becomes:
\[ \int \sec^2 x \, dx \]

### Step 3: Integrate
The integral of \( \sec^2 x \) is a standard integral:
\[ \int \sec^2 x \, dx = \tan x + C \]
where \( C \) is the constant of integration.

### Final Answer
Putting it all together, we find:
\[ \int \frac{dx}{1 - \sin^2 x} = \tan x + C \]

---