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Solving integrals/ arctg^6x-1

Integral of arctg^6x-1 dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1                  
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 |  /    6       \   
 |  \atan (x) - 1/ dx
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0
$$\int\limits_{0}^{1} \left(\operatorname{atan}^{6}{\left(x \right)} - 1\right)\, dx$$ 
Integral(atan(x)^6 - 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      But the integral is

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

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              /           
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 | /    6       \               |     6      
 | \atan (x) - 1/ dx = C - x +  | atan (x) dx
 |                              |            
/                              /
$$\int \left(\operatorname{atan}^{6}{\left(x \right)} - 1\right)\, dx = C - x + \int \operatorname{atan}^{6}{\left(x \right)}\, dx$$
Simplify
The answer [src] 
  1                                                                                  
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 |                               /        2             \ /        2             \   
 |  (1 + atan(x))*(-1 + atan(x))*\1 + atan (x) - atan(x)/*\1 + atan (x) + atan(x)/ dx
 |                                                                                   
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0
$$\int\limits_{0}^{1} \left(\operatorname{atan}{\left(x \right)} - 1\right) \left(\operatorname{atan}{\left(x \right)} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} - \operatorname{atan}{\left(x \right)} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + \operatorname{atan}{\left(x \right)} + 1\right)\, dx$$ 
=
= 
  1                                                                                  
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 |                               /        2             \ /        2             \   
 |  (1 + atan(x))*(-1 + atan(x))*\1 + atan (x) - atan(x)/*\1 + atan (x) + atan(x)/ dx
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0
$$\int\limits_{0}^{1} \left(\operatorname{atan}{\left(x \right)} - 1\right) \left(\operatorname{atan}{\left(x \right)} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} - \operatorname{atan}{\left(x \right)} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + \operatorname{atan}{\left(x \right)} + 1\right)\, dx$$ 
Integral((1 + atan(x))*(-1 + atan(x))*(1 + atan(x)^2 - atan(x))*(1 + atan(x)^2 + atan(x)), (x, 0, 1))
Numerical answer [src] 
-0.955043511201883
-0.955043511201883

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

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