One key idea to use in order to make the question simpler is by using trigonometric identity. As 1 + cot^2(x) = csc^2(x), cot^2(x) can be substituted as csc^2(x) - 1.
Now, calculate the integral using integration rules.
Remember, as the derivative of cot(x) is csc^2(x), the antiderivative of csc^2(x) is cot(x).
Hi,
Thank you for your question.
One key idea to use in order to make the question simpler is by using trigonometric identity. As 1 + cot^2(x) = csc^2(x), cot^2(x) can be substituted as csc^2(x) - 1.
Now, calculate the integral using integration rules.
Remember, as the derivative of cot(x) is csc^2(x), the antiderivative of csc^2(x) is cot(x).
∫csc^2(x) - 1 dx
= - cot(x) - x + C.
Hence, your answer would be - cot(x) - x + C.
Does this answer your question?