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Solving integrals/ 1/(3cos(5x-(pi/4)))

Integral of 1/(3cos(5x-(pi/4))) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |       /      pi\   
 |  3*cos|5*x - --|   
 |       \      4 /   
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{1}{3 \cos{\left(5 x - \frac{\pi}{4} \right)}}\, dx$$ 
Integral(1/(3*cos(5*x - pi/4)), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            /   /pi   5*x\\
 |                          log|tan|-- + ---||
 |        1                    \   \8     2 //
 | --------------- dx = C + ------------------
 |      /      pi\                  15        
 | 3*cos|5*x - --|                            
 |      \      4 /                            
 |                                            
/
$$\int \frac{1}{3 \cos{\left(5 x - \frac{\pi}{4} \right)}}\, dx = C + \frac{\log{\left(\tan{\left(\frac{5 x}{2} + \frac{\pi}{8} \right)} \right)}}{15}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                       /   /5   pi\\
     /       ___\   log|tan|- + --||
  log\-1 + \/ 2 /      \   \2   8 //
- --------------- + ----------------
         15                15
$$- \frac{\log{\left(-1 + \sqrt{2} \right)}}{15} + \frac{\log{\left(\tan{\left(\frac{\pi}{8} + \frac{5}{2} \right)} \right)}}{15}$$ 
=
= 
                       /   /5   pi\\
     /       ___\   log|tan|- + --||
  log\-1 + \/ 2 /      \   \2   8 //
- --------------- + ----------------
         15                15
$$- \frac{\log{\left(-1 + \sqrt{2} \right)}}{15} + \frac{\log{\left(\tan{\left(\frac{\pi}{8} + \frac{5}{2} \right)} \right)}}{15}$$ 
-log(-1 + sqrt(2))/15 + log(tan(5/2 + pi/8))/15
Numerical answer [src] 
-0.142838283888503
-0.142838283888503

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

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