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Solving integrals/ cosxsqrt1+sinx

Integral of cosxsqrt1+sinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 e2                           
  /                           
 |                            
 |  /         ___         \   
 |  \cos(x)*\/ 1  + sin(x)/ dx
 |                            
/                             
E
$$\int\limits_{e}^{e_{2}} \left(\sin{\left(x \right)} + \sqrt{1} \cos{\left(x \right)}\right)\, dx$$ 
Integral(cos(x)*sqrt(1) + sin(x), (x, E, e2))
Detail solution

  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

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

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

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                
 |                                                 
 | /         ___         \                         
 | \cos(x)*\/ 1  + sin(x)/ dx = C - cos(x) + sin(x)
 |                                                 
/
$$\int \left(\sin{\left(x \right)} + \sqrt{1} \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - \cos{\left(x \right)}$$
Simplify
The answer [src] 
-cos(e2) - sin(E) + cos(E) + sin(e2)
$$\sin{\left(e_{2} \right)} - \cos{\left(e_{2} \right)} + \cos{\left(e \right)} - \sin{\left(e \right)}$$ 
=
= 
-cos(e2) - sin(E) + cos(E) + sin(e2)
$$\sin{\left(e_{2} \right)} - \cos{\left(e_{2} \right)} + \cos{\left(e \right)} - \sin{\left(e \right)}$$ 
-cos(e2) - sin(E) + cos(E) + sin(e2)

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

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