Integral of arctg^6x-1 dx

You have entered [src]

  1                  
  /                  
 |                   
 |  /    6       \   
 |  \atan (x) - 1/ dx
 |                   
/                    
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

Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \operatorname{atan}^{6}{\left(x \right)}\, dx$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $- x + \int \operatorname{atan}^{6}{\left(x \right)}\, dx$
Add the constant of integration:

$- x + \int \operatorname{atan}^{6}{\left(x \right)}\, dx+ \mathrm{constant}$

The answer is:

$- x + \int \operatorname{atan}^{6}{\left(x \right)}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              /           
 |                              |            
 | /    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                                                                                  
  /                                                                                  
 |                                                                                   
 |                               /        2             \ /        2             \   
 |  (1 + atan(x))*(-1 + atan(x))*\1 + atan (x) - atan(x)/*\1 + atan (x) + atan(x)/ dx
 |                                                                                   
/                                                                                    
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                                                                                  
  /                                                                                  
 |                                                                                   
 |                               /        2             \ /        2             \   
 |  (1 + atan(x))*(-1 + atan(x))*\1 + atan (x) - atan(x)/*\1 + atan (x) + atan(x)/ dx
 |                                                                                   
/                                                                                    
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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of arctg^6x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution