\( \int \frac{\text { Factor the diferonce of two squaros. }}{36-x^{2}} 33-x^{2}=\square \)

Calculate or simplify the expression \( \int \frac{33-x^{2}}{36-x^{2}} \). Evaluate the integral by following steps: - step0: Evaluate using formulas and rules: \(\int \frac{33-x^{2}}{36-x^{2}} dx\) - step1: Rearrange the terms: \(\int -\frac{33-x^{2}}{x^{2}-36} dx\) - step2: Rewrite the fraction: \(\int -\left(-1-\frac{3}{x^{2}-36}\right) dx\) - step3: Calculate: \(\int \left(1+\frac{3}{x^{2}-36}\right) dx\) - step4: Use properties of integrals: \(\int 1 dx+\int \frac{3}{x^{2}-36} dx\) - step5: Evaluate the integral: \(x+\int \frac{3}{x^{2}-36} dx\) - step6: Evaluate the integral: \(x+\frac{1}{4}\ln{\left(\left|x-6\right|\right)}-\frac{1}{4}\ln{\left(\left|x+6\right|\right)}\) - step7: Subtract the terms: \(x+\frac{1}{4}\ln{\left(\frac{\left|x-6\right|}{\left|x+6\right|}\right)}\) - step8: Add the constant of integral C: \(x+\frac{1}{4}\ln{\left(\frac{\left|x-6\right|}{\left|x+6\right|}\right)} + C, C \in \mathbb{R}\) The integral of \( \frac{33-x^{2}}{36-x^{2}} \) with respect to \( x \) is given by: \[ \int \frac{33-x^{2}}{36-x^{2}} dx = x + \frac{1}{4} \ln\left(\frac{|x-6|}{|x+6|}\right) + C \] where \( C \) is the constant of integration.