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sin2x/(1+sin^2x)

Integral of sin2x/(1+sin^2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |    sin(2*x)    
 |  ----------- dx
 |         2      
 |  1 + sin (x)   
 |                
/                 
0                 
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)} + 1}\, dx$$
Integral(sin(2*x)/(1 + sin(x)^2), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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 .

          So, the result is:

        Now substitute back in:

      So, the result is:

    Method #2

    1. Rewrite the integrand:

    2. 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 .

          So, the result is:

        Now substitute back in:

      So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                     
 |                                      
 |   sin(2*x)              /       2   \
 | ----------- dx = C + log\1 + sin (x)/
 |        2                             
 | 1 + sin (x)                          
 |                                      
/                                       
$$\log \left(\sin ^2x+1\right)$$
The graph
The answer [src]
   /       2   \
log\1 + sin (1)/
$$\log \left(\sin ^21+1\right)$$
=
=
   /       2   \
log\1 + sin (1)/
$$\log{\left(\sin^{2}{\left(1 \right)} + 1 \right)}$$
Numerical answer [src]
0.53536607938024
0.53536607938024
The graph
Integral of sin2x/(1+sin^2x) dx

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