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Solving integrals/ sinx/(5cosx+3)

Integral of sinx/(5cosx+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     sin(x)      
 |  ------------ dx
 |  5*cos(x) + 3   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{5 \cos{\left(x \right)} + 3}\, dx$$ 
Integral(sin(x)/(5*cos(x) + 3), (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 is .

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                       
 |                                        
 |    sin(x)             log(5*cos(x) + 3)
 | ------------ dx = C - -----------------
 | 5*cos(x) + 3                  5        
 |                                        
/
$$\int \frac{\sin{\left(x \right)}}{5 \cos{\left(x \right)} + 3}\, dx = C - \frac{\log{\left(5 \cos{\left(x \right)} + 3 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  log(3/5 + cos(1))   log(8/5)
- ----------------- + --------
          5              5
$$- \frac{\log{\left(\cos{\left(1 \right)} + \frac{3}{5} \right)}}{5} + \frac{\log{\left(\frac{8}{5} \right)}}{5}$$ 
=
= 
  log(3/5 + cos(1))   log(8/5)
- ----------------- + --------
          5              5
$$- \frac{\log{\left(\cos{\left(1 \right)} + \frac{3}{5} \right)}}{5} + \frac{\log{\left(\frac{8}{5} \right)}}{5}$$ 
-log(3/5 + cos(1))/5 + log(8/5)/5
Numerical answer [src] 
0.0677420442814802
0.0677420442814802

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

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