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Integral of d{x}:
Integral of 1/e^x
Integral of sin(x)/cos(x)
Integral of dx/sinx
Integral of |-1+x|
Identical expressions
x^ five -arctg^ two (x)/(x^ six +7x+ four)
x to the power of 5 minus arctg squared (x) divide by (x to the power of 6 plus 7x plus 4)
x to the power of five minus arctg to the power of two (x) divide by (x to the power of six plus 7x plus four)
x5-arctg2(x)/(x6+7x+4)
x5-arctg2x/x6+7x+4
x⁵-arctg²(x)/(x⁶+7x+4)
x to the power of 5-arctg to the power of 2(x)/(x to the power of 6+7x+4)
x^5-arctg^2x/x^6+7x+4
x^5-arctg^2(x) divide by (x^6+7x+4)
x^5-arctg^2(x)/(x^6+7x+4)dx
Similar expressions
x^5-arctg^2(x)/(x^6-7x+4)
x^5+arctg^2(x)/(x^6+7x+4)
x^5-arctg^2(x)/(x^6+7x-4)

Solving integrals/ x^5-arctg^2(x)/(x^6+7x+4)

Integral of x^5-arctg^2(x)/(x^6+7x+4) dx

The solution

You have entered [src]

 oo                       
  /                       
 |                        
 |  /           2     \   
 |  | 5     atan (x)  |   
 |  |x  - ------------| dx
 |  |      6          |   
 |  \     x  + 7*x + 4/   
 |                        
/                         
1

$$\int\limits_{1}^{\infty} \left(x^{5} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\right)\, dx$$

Integral(x^5 - atan(x)^2/(x^6 + 7*x + 4), (x, 1, oo))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{5}\, dx = \frac{x^{6}}{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\right)\, dx = - \int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx$
  So, the result is: $- \int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx$
The result is: $\frac{x^{6}}{6} - \int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx$
Add the constant of integration:

$\frac{x^{6}}{6} - \int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx+ \mathrm{constant}$

The answer is:

$\frac{x^{6}}{6} - \int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               /                    
 |                               |                     
 | /           2     \           |       2            6
 | | 5     atan (x)  |           |   atan (x)        x 
 | |x  - ------------| dx = C -  | ------------ dx + --
 | |      6          |           |      6            6 
 | \     x  + 7*x + 4/           | 4 + x  + 7*x        
 |                               |                     
/                               /

$${{x^6}\over{6}}-\int {{{\arctan ^2x}\over{x^6+7\,x+4}}}{\;dx}$$

The answer [src]

 oo                                
  /                                
 |                                 
 |   11       2         5      6   
 |  x   - atan (x) + 4*x  + 7*x    
 |  ---------------------------- dx
 |               6                 
 |          4 + x  + 7*x           
 |                                 
/                                  
1

$$\int_{1}^{{\it oo}}{x^5-{{\arctan ^2x}\over{x^6+7\,x+4}}\;dx}$$

 oo                                
  /                                
 |                                 
 |   11       2         5      6   
 |  x   - atan (x) + 4*x  + 7*x    
 |  ---------------------------- dx
 |               6                 
 |          4 + x  + 7*x           
 |                                 
/                                  
1

$$\int\limits_{1}^{\infty} \frac{x^{11} + 7 x^{6} + 4 x^{5} - \operatorname{atan}^{2}{\left(x \right)}}{x^{6} + 7 x + 4}\, dx$$

Simplify

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

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Integral of x^5-arctg^2(x)/(x^6+7x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution