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Solving integrals/ cos((2x+1)/5)

Integral of cos((2x+1)/5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     /2*x + 1\   
 |  cos|-------| dx
 |     \   5   /   
 |                 
/                  
0
$$\int\limits_{0}^{1} \cos{\left(\frac{2 x + 1}{5} \right)}\, dx$$ 
Integral(cos((2*x + 1)/5), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                           /2*x + 1\
 |                       5*sin|-------|
 |    /2*x + 1\               \   5   /
 | cos|-------| dx = C + --------------
 |    \   5   /                2       
 |                                     
/
$$\int \cos{\left(\frac{2 x + 1}{5} \right)}\, dx = C + \frac{5 \sin{\left(\frac{2 x + 1}{5} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  5*sin(1/5)   5*sin(3/5)
- ---------- + ----------
      2            2
$$- \frac{5 \sin{\left(\frac{1}{5} \right)}}{2} + \frac{5 \sin{\left(\frac{3}{5} \right)}}{2}$$ 
=
= 
  5*sin(1/5)   5*sin(3/5)
- ---------- + ----------
      2            2
$$- \frac{5 \sin{\left(\frac{1}{5} \right)}}{2} + \frac{5 \sin{\left(\frac{3}{5} \right)}}{2}$$ 
-5*sin(1/5)/2 + 5*sin(3/5)/2
Numerical answer [src] 
0.914932856499935
0.914932856499935

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

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