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Integral of sin(3x)/sqrt(cos(3x)) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |    sin(3*x)     
 |  ------------ dx
 |    __________   
 |  \/ cos(3*x)    
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{\sin{\left(3 x \right)}}{\sqrt{\cos{\left(3 x \right)}}}\, dx$$
Integral(sin(3*x)/sqrt(cos(3*x)), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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. 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 is when :

            So, the result is:

          Now substitute back in:

        So, the result is:

      Now substitute back in:

    Method #2

    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 a constant is the constant times the variable of integration:

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                    
 |                           __________
 |   sin(3*x)            2*\/ cos(3*x) 
 | ------------ dx = C - --------------
 |   __________                3       
 | \/ cos(3*x)                         
 |                                     
/                                      
$$\int \frac{\sin{\left(3 x \right)}}{\sqrt{\cos{\left(3 x \right)}}}\, dx = C - \frac{2 \sqrt{\cos{\left(3 x \right)}}}{3}$$
The graph
The answer [src]
        ________
2   2*\/ cos(3) 
- - ------------
3        3      
$$\frac{2}{3} - \frac{2 \sqrt{\cos{\left(3 \right)}}}{3}$$
=
=
        ________
2   2*\/ cos(3) 
- - ------------
3        3      
$$\frac{2}{3} - \frac{2 \sqrt{\cos{\left(3 \right)}}}{3}$$
2/3 - 2*sqrt(cos(3))/3
Numerical answer [src]
(0.579862216335156 - 0.795858425143173j)
(0.579862216335156 - 0.795858425143173j)

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