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Integral of ((tg7x)^4)/(cos7x)^2 dx

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The solution

You have entered [src]
  1             
  /             
 |              
 |     4        
 |  tan (7*x)   
 |  --------- dx
 |     2        
 |  cos (7*x)   
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{\tan^{4}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}}\, dx$$
Integral(tan(7*x)^4/cos(7*x)^2, (x, 0, 1))
The answer (Indefinite) [src]
  /                                                            
 |                                                             
 |    4                                                        
 | tan (7*x)           2*sin(7*x)      sin(7*x)      sin(7*x)  
 | --------- dx = C - ------------ + ----------- + ------------
 |    2                     3        35*cos(7*x)         5     
 | cos (7*x)          35*cos (7*x)                 35*cos (7*x)
 |                                                             
/                                                              
$$\int \frac{\tan^{4}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}}\, dx = C + \frac{\sin{\left(7 x \right)}}{35 \cos{\left(7 x \right)}} - \frac{2 \sin{\left(7 x \right)}}{35 \cos^{3}{\left(7 x \right)}} + \frac{\sin{\left(7 x \right)}}{35 \cos^{5}{\left(7 x \right)}}$$
The graph
The answer [src]
  1             
  /             
 |              
 |     4        
 |  tan (7*x)   
 |  --------- dx
 |     2        
 |  cos (7*x)   
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{\tan^{4}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}}\, dx$$
=
=
  1             
  /             
 |              
 |     4        
 |  tan (7*x)   
 |  --------- dx
 |     2        
 |  cos (7*x)   
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{\tan^{4}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}}\, dx$$
Integral(tan(7*x)^4/cos(7*x)^2, (x, 0, 1))
Numerical answer [src]
87995458.3854997
87995458.3854997

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