cscx cotx dx
The expression cscx cotx dx represents an indefinite integral
The expression cscx cotx dx represents an indefinite integral. To evaluate this integral, we can use the trigonometric identity cscx = 1/sinx and cotx = cosx/sinx.
First, let’s rewrite the integral using the identities:
∫ (1/sinx)(cosx/sinx) dx
Next, we can simplify this expression by multiplying the two fractions:
∫ (cosx)/(sin^2x) dx
Now, we can use a substitution to simplify the integral. Let’s substitute u = sinx, then du = cosx dx. This transforms the integral as follows:
∫ (1/u^2) du
Integrating this expression gives:
∫ u^(-2) du = -u^(-1) + C
where C is the constant of integration.
Finally, substituting u back with sinx, we have:
– (sinx)^(-1) + C
This can also be written as:
– cscx + C
Therefore, the integral of cscx cotx dx is -cscx + C, where C is the constant of integration.
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