Answer:
Step-by-step explanation:
To integrate the expression (sin²x-cos²x) dx / (sin²x cosx), we can use the following steps:
Rewrite the numerator as -cos(2x).
Rewrite the denominator as cos²x - sin²x.
Use the identity cos²x - sin²x = cos(2x) to simplify the denominator.
Substitute u = sin(x) and du = cos(x) dx to transform the integral into -∫ du/u.
Integrate -ln|u| + C concerning u.
Substitute back u = sin(x) to get the final answer: -ln|sin(x)| + C.
Therefore, the integral of (sin²x-cos²x) dx / (sin²x cosx) is equal to -ln|sin(x)| + C.
