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ctg(x)^4+ctg(x)^2
Solving integrals/ ctg(x)^4+ctg(x)^2

Integral of ctg(x)^4+ctg(x)^2 dx

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The solution

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∫01(cot⁡4(x)+cot⁡2(x)) dx\int\limits_{0}^{1} \left(\cot^{4}{\left(x \right)} + \cot^{2}{\left(x \right)}\right)\, dx 
Integral(cot(x)^4 + cot(x)^2, (x, 0, 1))
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)−cos⁡3(x)3sin⁡3(x)x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}

    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)}}

    The result is: −cos⁡3(x)3sin⁡3(x)- \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}

  2. Now simplify:

    −13tan⁡3(x)- \frac{1}{3 \tan^{3}{\left(x \right)}}

  3. Add the constant of integration:

    −13tan⁡3(x)+constant- \frac{1}{3 \tan^{3}{\left(x \right)}}+ \mathrm{constant}

The answer is:

−13tan⁡3(x)+constant- \frac{1}{3 \tan^{3}{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                      
 |                                  3    
 | /   4         2   \           cos (x) 
 | \cot (x) + cot (x)/ dx = C - ---------
 |                                   3   
/                               3*sin (x)
∫(cot⁡4(x)+cot⁡2(x)) dx=C−cos⁡3(x)3sin⁡3(x)\int \left(\cot^{4}{\left(x \right)} + \cot^{2}{\left(x \right)}\right)\, dx = C - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-50000000000000005000000000000000
Plot the graph f(x)
The answer [src] 
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∞\infty 
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∞\infty
Упростить
Numerical answer [src] 
7.81431122445857e+56
7.81431122445857e+56
The graph
Integral of ctg(x)^4+ctg(x)^2 dx

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

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