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Integral of (cos(x)+1)/sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  cos(x) + 1   
 |  ---------- dx
 |    sin(x)     
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)} + 1}{\sin{\left(x \right)}}\, dx$$
Integral((cos(x) + 1)/sin(x), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

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

      But the integral is

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                    
 |                                                                     
 | cos(x) + 1          log(-1 + cos(x))   log(1 + cos(x))              
 | ---------- dx = C + ---------------- - --------------- + log(sin(x))
 |   sin(x)                   2                  2                     
 |                                                                     
/                                                                      
$$\int \frac{\cos{\left(x \right)} + 1}{\sin{\left(x \right)}}\, dx = C + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} + \log{\left(\sin{\left(x \right)} \right)}$$
The graph
The answer [src]
oo
$$\infty$$
=
=
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$$\infty$$
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Numerical answer [src]
88.096853256335
88.096853256335

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