Solving the Integral of cot(u) du using Integration by Substitution

∫ cotu du

To solve the integral of cot(u) du, we can use a technique called integration by substitution

To solve the integral of cot(u) du, we can use a technique called integration by substitution. We will perform the following steps:

Step 1: Let’s start by considering the integral ∫ cot(u) du.

Step 2: Notice that the derivative of cot(u) is -cosec^2(u) du. We don’t have exactly that in our integral, but we have a similar term cot(u).

Step 3: To simplify our integral, we can rewrite cot(u) as cos(u)/sin(u). Now our integral becomes ∫ (cos(u)/sin(u)) du.

Step 4: Next, we will substitute a new variable to make the integral easier. Let’s define v = sin(u), so that dv = cos(u) du.

Step 5: Substituting these values, we have ∫ (1/v) dv.

Step 6: Integrating 1/v with respect to v gives us ln|v| + C, where C is the constant of integration.

Step 7: Going back to our original variable, we substitute v with sin(u) to find that ∫ (cot(u) du) = ln|sin(u)| + C.

Therefore, the solution to the integral of cot(u) du is ln|sin(u)| + C, where C represents the constant of integration.

More Answers: