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Solving integrals/ 1/sinx+cosx

Integral of 1/sinx+cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of cosine is sine:

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

      But the integral is

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                        
 |                                                                         
 | /    1            \          log(-1 + cos(x))   log(1 + cos(x))         
 | |1*------ + cos(x)| dx = C + ---------------- - --------------- + sin(x)
 | \  sin(x)         /                 2                  2                
 |                                                                         
/
$$-{{\log \left(\cos x+1\right)}\over{2}}+{{\log \left(\cos x-1 \right)}\over{2}}+\sin x$$
Simplify
The answer [src] 
     pi*I
oo + ----
      2
$${\it \%a}$$ 
=
= 
     pi*I
oo + ----
      2
$$\infty + \frac{i \pi}{2}$$
Simplify
Numerical answer [src] 
45.0204818534191
45.0204818534191

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

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