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Solving integrals/ 1+cot^2(x)

Integral of 1+cot^2(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫π4π2(cot⁡2(x)+1) dx\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)\, dx 
Integral(1 + cot(x)^2, (x, pi/4, pi/2))
Detail solution

  1. Integrate term-by-term:

    1. Don't know the steps in finding this integral.

      But the integral is

      −x−cos⁡(x)sin⁡(x)- x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

    The result is: −cos⁡(x)sin⁡(x)- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

  2. Now simplify:

    −1tan⁡(x)- \frac{1}{\tan{\left(x \right)}}

  3. Add the constant of integration:

    −1tan⁡(x)+constant- \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer is:

−1tan⁡(x)+constant- \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 | /       2   \          cos(x)
 | \1 + cot (x)/ dx = C - ------
 |                        sin(x)
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∫(cot⁡2(x)+1) dx=C−cos⁡(x)sin⁡(x)\int \left(\cot^{2}{\left(x \right)} + 1\right)\, dx = C - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}
Simplify
The graph
0.800.850.900.951.001.051.101.151.201.251.301.351.401.451.501.555-5
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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