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Integral of (x^2)/(1+x^6)
Identical expressions
(x^ two)/(one +x^ six)
(x squared ) divide by (1 plus x to the power of 6)
(x to the power of two) divide by (one plus x to the power of six)
(x2)/(1+x6)
x2/1+x6
(x²)/(1+x⁶)
(x to the power of 2)/(1+x to the power of 6)
x^2/1+x^6
(x^2) divide by (1+x^6)
(x^2)/(1+x^6)dx
Similar expressions
(x^2)/(1-x^6)

Solving integrals/ (x^2)/(1+x^6)

Integral of (x^2)/(1+x^6) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |       6   
 |  1 + x    
 |           
/            
0

$$\int\limits_{0}^{1} \frac{x^{2}}{x^{6} + 1}\, dx$$

Integral(x^2/(1 + x^6), (x, 0, 1))

Detail solution

Let $u = x^{3}$ .

Then let $du = 3 x^{2} dx$ and substitute $du$ :

$\int \frac{1}{3 u^{2} + 3}\, du$
1. The integral of $\frac{1}{u^{2} + 1}$ is $\frac{\operatorname{atan}{\left(u \right)}}{3}$ .
Now substitute $u$ back in:

$\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}$
Add the constant of integration:

$\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 |    2                / 3\
 |   x             atan\x /
 | ------ dx = C + --------
 |      6             3    
 | 1 + x                   
 |                         
/

$${{\arctan x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi
--
12

$${{\pi}\over{12}}$$

pi
--
12

$$\frac{\pi}{12}$$

Упростить

Numerical answer [src]

0.261799387799149

0.261799387799149

The graph

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

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Identical expressions

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Integral of (x^2)/(1+x^6) dx

Limits of integration:

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Piecewise:

The solution