Integral of cosecx dx
The solution
Detail solution
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Rewrite the integrand:
csc(x)=cot(x)+csc(x)cot(x)csc(x)+csc2(x)
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Let u=cot(x)+csc(x).
Then let du=(−cot2(x)−cot(x)csc(x)−1)dx and substitute −du:
∫(−u1)du
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The integral of a constant times a function is the constant times the integral of the function:
∫u1du=−∫u1du
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The integral of u1 is log(u).
So, the result is: −log(u)
Now substitute u back in:
−log(cot(x)+csc(x))
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Add the constant of integration:
−log(cot(x)+csc(x))+constant
The answer is:
−log(cot(x)+csc(x))+constant
The answer (Indefinite)
[src]
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| csc(x) dx = C - log(cot(x) + csc(x))
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∫csc(x)dx=C−log(cot(x)+csc(x))
The graph
∞+2iπ
=
∞+2iπ
Use the examples entering the upper and lower limits of integration.