26. \( \int \frac{d x}{\operatorname{sen}^{2} x \cdot \cos ^{2} x} \)

Calculate the integral \( \int \frac{1}{\sin^2(x) \cos^2(x)} dx \). Evaluate the integral by following steps: - step0: Evaluate using formulas and rules: \(\int \frac{1}{\sin^{2}\left(x\right)\cos^{2}\left(x\right)} dx\) - step1: Multiply the terms: \(\int \frac{1}{\left(\sin\left(x\right)\cos\left(x\right)\right)^{2}} dx\) - step2: Rewrite the expression: \(\int 4\sin^{-2}\left(2x\right) dx\) - step3: Rewrite the expression: \(\int \frac{4}{\sin^{2}\left(2x\right)} dx\) - step4: Rewrite the expression: \(\int 4\times \frac{1}{\sin^{2}\left(2x\right)} dx\) - step5: Use properties of integrals: \(4\times \int \frac{1}{\sin^{2}\left(2x\right)} dx\) - step6: Evaluate the integral: \(4\left(-\frac{1}{2}\right)\cot\left(2x\right)\) - step7: Calculate: \(4\left(-\frac{1}{2}\cot\left(2x\right)\right)\) - step8: Rewrite the expression: \(-4\times \frac{1}{2}\cot\left(2x\right)\) - step9: Multiply the terms: \(-2\cot\left(2x\right)\) - step10: Add the constant of integral C: \(-2\cot\left(2x\right) + C, C \in \mathbb{R}\) La integral de \( \frac{1}{\sin^2(x) \cos^2(x)} \) con respecto a \( x \) es \( -2\cot(2x) + C \), donde \( C \) es una constante real.