How to Find the Antiderivative of csc(x)cot(x) using the Substitution Method

Antiderivative cscxcotx

To find the antiderivative of csc(x)cot(x), we can use the substitution method

To find the antiderivative of csc(x)cot(x), we can use the substitution method.

Let’s start by rewriting the expression as:

csc(x)cot(x) = (1/sin(x))(cos(x)/sin(x))

We can make the substitution u = sin(x). Then, du = cos(x) dx.

Using this substitution, we can rewrite the expression as:

(1/u)(du)

Now, we have simplified the expression into a form that is easier to integrate.

The integral of (1/u) du is ln|u| + C, where C is the constant of integration.

Replacing the value of u back with sin(x), we have:

ln|sin(x)| + C

Therefore, the antiderivative of csc(x)cot(x) is ln|sin(x)| + C, where C is the constant of integration.

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