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tg^6x
Solving integrals/ tg^6x

Integral of tg^6x dx

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The solution

You have entered [src] 
  1           
  /           
 |            
 |     6      
 |  tan (x) dx
 |            
/             
0
$$\int\limits_{0}^{1} \tan^{6}{\left(x \right)}\, dx$$ 
Integral(tan(x)^6, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                   3           5    
 |    6                 sin(x)    sin (x)     sin (x) 
 | tan (x) dx = C - x + ------ - --------- + ---------
 |                      cos(x)        3           5   
/                                3*cos (x)   5*cos (x)
$$\int \tan^{6}{\left(x \right)}\, dx = C - x + \frac{\sin^{5}{\left(x \right)}}{5 \cos^{5}{\left(x \right)}} - \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                  3           5    
     sin(1)    sin (1)     sin (1) 
-1 + ------ - --------- + ---------
     cos(1)        3           5   
              3*cos (1)   5*cos (1)
$$- \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}}$$ 
=
= 
                  3           5    
     sin(1)    sin (1)     sin (1) 
-1 + ------ - --------- + ---------
     cos(1)        3           5   
              3*cos (1)   5*cos (1)
$$- \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}}$$ 
-1 + sin(1)/cos(1) - sin(1)^3/(3*cos(1)^3) + sin(1)^5/(5*cos(1)^5)
Numerical answer [src] 
1.13072382779173
1.13072382779173
The graph
Integral of tg^6x dx

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

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