∫csc²xdx
To find the integral of csc^2(x)dx, we can use a trigonometric identity to simplify the expression
To find the integral of csc^2(x)dx, we can use a trigonometric identity to simplify the expression.
The trigonometric identity we will use is:
1 + cot^2(x) = csc^2(x)
Rearranging this identity, we get:
cot^2(x) = csc^2(x) – 1
Now, let’s rewrite the integral using this identity:
∫csc^2(x)dx = ∫(csc^2(x) – 1)dx
The first term ∫csc^2(x)dx can be easily found. It is equal to -cot(x):
∫csc^2(x)dx = -cot(x) + C
Where C is the constant of integration.
Therefore, the integral of csc^2(x)dx is -cot(x) + C.
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