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Integral of 1/sin^2x+4cos^2x dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                         
 --                         
 4                          
  /                         
 |                          
 |  /   1           2   \   
 |  |------- + 4*cos (x)| dx
 |  |   2               |   
 |  \sin (x)            /   
 |                          
/                           
0                           
$$\int\limits_{0}^{\frac{\pi}{4}} \left(4 \cos^{2}{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx$$
Integral(1/(sin(x)^2) + 4*cos(x)^2, (x, 0, pi/4))
Detail solution
  1. Integrate term-by-term:

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

      1. Rewrite the integrand:

      2. Integrate term-by-term:

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

          1. Let .

            Then let and substitute :

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

              1. The integral of cosine is sine:

              So, the result is:

            Now substitute back in:

          So, the result is:

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

        The result is:

      So, the result is:

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

      But the integral is

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                      
 |                                                       
 | /   1           2   \                cos(x)           
 | |------- + 4*cos (x)| dx = C + 2*x - ------ + sin(2*x)
 | |   2               |                sin(x)           
 | \sin (x)            /                                 
 |                                                       
/                                                        
$$\int \left(4 \cos^{2}{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = C + 2 x + \sin{\left(2 x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
The graph
The answer [src]
oo
$$\infty$$
=
=
oo
$$\infty$$
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Numerical answer [src]
1.75598925958649e+19
1.75598925958649e+19

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