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  • Identical expressions

  • atan^ two (x)/x^ seven
  • arc tangent of gent of squared (x) divide by x to the power of 7
  • arc tangent of gent of to the power of two (x) divide by x to the power of seven
  • atan2(x)/x7
  • atan2x/x7
  • atan²(x)/x⁷
  • atan to the power of 2(x)/x to the power of 7
  • atan^2x/x^7
  • atan^2(x) divide by x^7
  • atan^2(x)/x^7dx
Solving integrals/ atan^2(x)/x^7

Integral of atan^2(x)/x^7 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo            
  /            
 |             
 |      2      
 |  atan (x)   
 |  -------- dx
 |      7      
 |     x       
 |             
/              
1
$$\int\limits_{1}^{\infty} \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{7}}\, dx$$ 
Integral(atan(x)^2/x^7, (x, 1, oo))
The answer (Indefinite) [src] 
  /                                                                                                                
 |                                                                                                                 
 |     2                   /     2\       2                                                2                       
 | atan (x)          23*log\1 + x /   atan (x)     1       4     23*log(x)   atan(x)   atan (x)   atan(x)   atan(x)
 | -------- dx = C - -------------- - -------- - ----- + ----- + --------- - ------- - -------- - ------- + -------
 |     7                   90            6           4       2       45        3*x          6          5         3 
 |    x                                          60*x    45*x                            6*x       15*x       9*x  
 |                                                                                                                 
/
$$\int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{7}}\, dx = C + \frac{23 \log{\left(x \right)}}{45} - \frac{23 \log{\left(x^{2} + 1 \right)}}{90} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{6} - \frac{\operatorname{atan}{\left(x \right)}}{3 x} + \frac{4}{45 x^{2}} + \frac{\operatorname{atan}{\left(x \right)}}{9 x^{3}} - \frac{1}{60 x^{4}} - \frac{\operatorname{atan}{\left(x \right)}}{15 x^{5}} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{6 x^{6}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          2                    
   13   pi    13*pi   23*log(2)
- --- - --- + ----- + ---------
  180    48    180        90
$$- \frac{\pi^{2}}{48} - \frac{13}{180} + \frac{23 \log{\left(2 \right)}}{90} + \frac{13 \pi}{180}$$ 
=
= 
          2                    
   13   pi    13*pi   23*log(2)
- --- - --- + ----- + ---------
  180    48    180        90
$$- \frac{\pi^{2}}{48} - \frac{13}{180} + \frac{23 \log{\left(2 \right)}}{90} + \frac{13 \pi}{180}$$ 
-13/180 - pi^2/48 + 13*pi/180 + 23*log(2)/90

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

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