∫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.
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