- #1
expscv
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hi all, but how do i intergrate
(cot(x))^2
thx
(cot(x))^2
thx
The integration formula for (cot(x))^2 is ∫(cot(x))^2 dx = -x - cot(x) + C.
To solve the integral of (cot(x))^2, you can use the substitution method by letting u = cot(x) and du = -csc^2(x) dx. This will result in the integral becoming ∫u^2 du, which can be easily solved using the power rule for integration.
The steps for integrating (cot(x))^2 using the substitution method are:
1. Let u = cot(x) and du = -csc^2(x) dx.
2. Rewrite the integral as ∫u^2 du.
3. Integrate u^2 using the power rule, resulting in u^3/3.
4. Substitute back in u = cot(x) to get the final solution of -cot^3(x)/3 + C.
Yes, you can use the inverse trigonometric substitution method by letting x = arccot(u) and dx = -du/(1+u^2). This will result in the integral becoming ∫(1+u^2)du, which again can be easily solved using the power rule for integration.
Yes, there is a special case when x = π/2 + πn, where n is any integer. In this case, the integral of (cot(x))^2 is undefined since cot(π/2 + πn) is undefined. This is because cot(x) is equal to 0 when x = π/2 + πn, making (cot(x))^2 undefined at these points.