A Comprehensive Guide to Integrating csc(x)cot(x) and its Definite Integral

∫csc(x)cot(x)dx

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

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

Let u = cot(x)
Then, du = -csc^2(x)dx
Rearranging, dx = -du/csc^2(x)

Now, let’s substitute these values into the integral:

∫csc(x)cot(x)dx = ∫csc(x)(u)(-du/csc^2(x))
= -∫u du
= -∫cot(x) du
= -∫u du
= -u^2/2 + C

Finally, substituting u back in terms of x:

= -cot^2(x)/2 + C

So, the definite integral of csc(x)cot(x)dx is given by -cot^2(x)/2 + C, where C is the constant of integration.

More Answers:

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How to Integrate the Function sec(x)tan(x) with Respect to x using U-Substitution

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