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sqrt(2+2cos(x))

Integral of sqrt(2+2cos(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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 |  \/ 2 + 2*cos(x)  dx
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$$\int\limits_{0}^{1} \sqrt{2 \cos{\left(x \right)} + 2}\, dx$$
Integral(sqrt(2 + 2*cos(x)), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. 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:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                                             _______________________________       
  /                                         /                        2/x\          
 |                                         /                      tan |-|          
 |   ______________              ___      /            1              \2/       /x\
 | \/ 2 + 2*cos(x)  dx = C + 2*\/ 2 *    /    1 + ----------- - ----------- *tan|-|
 |                                      /                2/x\          2/x\     \2/
/                                      /          1 + tan |-|   1 + tan |-|        
                                     \/                   \2/           \2/        
$${{4\,\sin x}\over{\left(\cos x+1\right)\,\sqrt{{{\sin ^2x}\over{ \left(\cos x+1\right)^2}}+1}}}$$
The graph
The answer [src]
$${{4\,\sqrt{\cos ^21+2\,\cos 1+1}\,\sin 1\,\sqrt{\sin ^21+\cos ^21+2 \,\cos 1+1}}\over{\left(\cos 1+1\right)\,\sin ^21+\cos ^31+3\,\cos ^ 21+3\,\cos 1+1}}$$
(4*sqrt(cos(1)^2+2*cos(1)+1)*sin(1)*sqrt(sin(1)^2+cos(1)^2+2*cos(1)+1))/((cos(1)+1)*sin(1)^2+cos(1)^3+3*cos(1)^2+3*cos(1)+1)
Numerical answer [src]
1.91770215441681
1.91770215441681
The graph
Integral of sqrt(2+2cos(x)) dx

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