We can integrate cotx using the method integration by substitution.
In trigonometry, we know the formula for cotx, that is
Integrate both sides with respect to x.
We know that the derivative sin x is cos x. In the integration above, cos x is multiplied by dx. Since the derivative of sin x is multiplied by dx, we can substitute a new variable y for sin x and continue the integration process.
Let y = sin x.
y = sinx
Find the derivative on both sides with respect to x.
Substitute sin x = y and cosx dx = dy in (1).
Substitute y = sin x.
Logarithm is not defined for zero or a negative value. So, we can use absolute value for sin x.
Therefore, integration of cot x is equal to ln|sinx| + c.
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