Answer: -ln |cos x| - ln |sin x| + C
Step-by-step explanation:
[tex].\quad \int\dfrac{sin^2x-cos^2x}{sin\ x\ cos\ x}dx\\\\\\=\int \dfrac{sin^2x}{sin\ x\ cos\ x}dx-\int \dfrac{cos^2x}{sin\ x\ cos\ x}dx\\\\\\=\int \dfrac{sin\ x}{cos\ x}dx-\int \dfrac{cos\ x}{sin\ x}dx\\\\\\=\int tan\ x\ dx - \int cot\ x\ dx\\\\=-ln |cos\ x|-ln|sin\ x| + C[/tex]
