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1/1+sinx+cosx
Solving integrals/ 1/1+sinx+cosx

Integral of 1/1+sinx+cosx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

    1. The integral of cosine is sine:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 | (1 + sin(x) + cos(x)) dx = C + x - cos(x) + sin(x)
 |                                                   
/
$$\sin x-\cos x+x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     pi
-2 - --
     2
$$-{{\pi+2\,\sin \left({{\pi}\over{2}}\right)-2\,\cos \left({{\pi }\over{2}}\right)+2}\over{2}}$$ 
=
= 
     pi
-2 - --
     2
$$-2 - \frac{\pi}{2}$$
Упростить
Numerical answer [src] 
-3.5707963267949
-3.5707963267949
The graph
Integral of 1/1+sinx+cosx dx

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

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