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Solving integrals/ tan(5x)^4

Integral of tan(5x)^4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |     4        
 |  tan (5*x) dx
 |              
/               
0
$$\int\limits_{0}^{1} \tan^{4}{\left(5 x \right)}\, dx$$ 
Integral(tan(5*x)^4, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                
 |                                         3       
 |    4                    sin(5*x)     sin (5*x)  
 | tan (5*x) dx = C + x - ---------- + ------------
 |                        5*cos(5*x)         3     
/                                      15*cos (5*x)
$$\int \tan^{4}{\left(5 x \right)}\, dx = C + x + \frac{\sin^{3}{\left(5 x \right)}}{15 \cos^{3}{\left(5 x \right)}} - \frac{\sin{\left(5 x \right)}}{5 \cos{\left(5 x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                   3     
     sin(5)     sin (5)  
1 - -------- + ----------
    5*cos(5)         3   
               15*cos (5)
$$\frac{\sin^{3}{\left(5 \right)}}{15 \cos^{3}{\left(5 \right)}} - \frac{\sin{\left(5 \right)}}{5 \cos{\left(5 \right)}} + 1$$ 
=
= 
                   3     
     sin(5)     sin (5)  
1 - -------- + ----------
    5*cos(5)         3   
               15*cos (5)
$$\frac{\sin^{3}{\left(5 \right)}}{15 \cos^{3}{\left(5 \right)}} - \frac{\sin{\left(5 \right)}}{5 \cos{\left(5 \right)}} + 1$$ 
1 - sin(5)/(5*cos(5)) + sin(5)^3/(15*cos(5)^3)
Numerical answer [src] 
5043537.44750744
5043537.44750744

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

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