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