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ctg(x)
Solving integrals/ ctg(x)

Integral of ctg(x) dx

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The solution

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∫01cot⁡(x) dx\int\limits_{0}^{1} \cot{\left(x \right)}\, dx 
Integral(cot(x), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    cot⁡(x)=cos⁡(x)sin⁡(x)\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

  2. Let u=sin⁡(x)u = \sin{\left(x \right)}.

    Then let du=cos⁡(x)dxdu = \cos{\left(x \right)} dx and substitute dudu:

    ∫1u du\int \frac{1}{u}\, du

    1. The integral of 1u\frac{1}{u} is log⁡(u)\log{\left(u \right)}.

    Now substitute uu back in:

    log⁡(sin⁡(x))\log{\left(\sin{\left(x \right)} \right)}

  3. Add the constant of integration:

    log⁡(sin⁡(x))+constant\log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}

The answer is:

log⁡(sin⁡(x))+constant\log{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫cot⁡(x) dx=C+log⁡(sin⁡(x))\int \cot{\left(x \right)}\, dx = C + \log{\left(\sin{\left(x \right)} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
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The answer [src] 
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∞\infty 
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Numerical answer [src] 
43.9178423877238
43.9178423877238
The graph
Integral of ctg(x) dx

    Use the examples entering the upper and lower limits of integration.

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