If `int 1/(1-sin^4x)dx=1/(asqrtb)+tan^(- 1)(sqrt(a)tanx)+1/btanx+C` then `a/b` is equal to

Explanation

To solve the given integral problem, we need to evaluate the integral \( I = \int \frac{1}{1 - \sin^4 x} \, dx \) and compare it to the expression provided in the question. Let's go through the steps systematically.

### Step 1: Rewrite the Integral
We start with:
\[ I = \int \frac{1}{1 - \sin^4 x} \, dx \]
We can use the identity \( \sin^4 x = (\sin^2 x)^2 \) to rewrite \( 1 - \sin^4 x \):
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