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Integral of d{x}:
Integral of e^(x^2)
Integral of sin(x)^3
Integral of √(x^2+1)
Integral of cos(5x)
Identical expressions
arctg^ six (x)/ six
arctg to the power of 6(x) divide by 6
arctg to the power of six (x) divide by six
arctg6(x)/6
arctg6x/6
arctg⁶(x)/6
arctg^6x/6
arctg^6(x) divide by 6
arctg^6(x)/6dx

Integral of arctg^6(x)/6 dx

The solution

You have entered [src]

  1            
  /            
 |             
 |      6      
 |  atan (x)   
 |  -------- dx
 |     6       
 |             
/              
0

$$\int\limits_{0}^{1} \frac{\operatorname{atan}^{6}{\left(x \right)}}{6}\, dx$$

Integral(atan(x)^6/6, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\operatorname{atan}^{6}{\left(x \right)}}{6}\, dx = \frac{\int \operatorname{atan}^{6}{\left(x \right)}\, dx}{6}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \operatorname{atan}^{6}{\left(x \right)}\, dx$
So, the result is: $\frac{\int \operatorname{atan}^{6}{\left(x \right)}\, dx}{6}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

                       /           
                      |            
  /                   |     6      
 |                    | atan (x) dx
 |     6              |            
 | atan (x)          /             
 | -------- dx = C + --------------
 |    6                    6       
 |                                 
/

$$\int \frac{\operatorname{atan}^{6}{\left(x \right)}}{6}\, dx = C + \frac{\int \operatorname{atan}^{6}{\left(x \right)}\, dx}{6}$$

Simplify

The answer [src]

  1            
  /            
 |             
 |      6      
 |  atan (x) dx
 |             
/              
0              
---------------
       6

$$\frac{\int\limits_{0}^{1} \operatorname{atan}^{6}{\left(x \right)}\, dx}{6}$$

  1            
  /            
 |             
 |      6      
 |  atan (x) dx
 |             
/              
0              
---------------
       6

$$\frac{\int\limits_{0}^{1} \operatorname{atan}^{6}{\left(x \right)}\, dx}{6}$$

Integral(atan(x)^6, (x, 0, 1))/6

Numerical answer [src]

0.00749274813301943

0.00749274813301943

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

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Identical expressions

Integral of arctg^6(x)/6 dx

Limits of integration:

The graph:

Piecewise:

The solution