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Solving integrals/ x×sinx/(4+tg^2x)

Integral of x×sinx/(4+tg^2x) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  pi               
  --               
  3                
   /               
  |                
  |    x*sin(x)    
  |  ----------- dx
  |         2      
  |  4 + tan (x)   
  |                
 /                 
-pi                
----               
 3
∫−π3π3xsin⁡(x)tan⁡2(x)+4 dx\int\limits_{- \frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\, dx 
Integral((x*sin(x))/(4 + tan(x)^2), (x, -pi/3, pi/3))
The answer (Indefinite) [src] 
  /                       /              
 |                       |               
 |   x*sin(x)            |   x*sin(x)    
 | ----------- dx = C +  | ----------- dx
 |        2              |        2      
 | 4 + tan (x)           | 4 + tan (x)   
 |                       |               
/                       /
∫xsin⁡(x)tan⁡2(x)+4 dx=C+∫xsin⁡(x)tan⁡2(x)+4 dx\int \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\, dx = C + \int \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\, dx
Simplify
The answer [src] 
  pi               
  --               
  3                
   /               
  |                
  |    x*sin(x)    
  |  ----------- dx
  |         2      
  |  4 + tan (x)   
  |                
 /                 
-pi                
----               
 3
∫−π3π3xsin⁡(x)tan⁡2(x)+4 dx\int\limits_{- \frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\, dx 
=
= 
  pi               
  --               
  3                
   /               
  |                
  |    x*sin(x)    
  |  ----------- dx
  |         2      
  |  4 + tan (x)   
  |                
 /                 
-pi                
----               
 3
∫−π3π3xsin⁡(x)tan⁡2(x)+4 dx\int\limits_{- \frac{\pi}{3}}^{\frac{\pi}{3}} \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\, dx 
Integral(x*sin(x)/(4 + tan(x)^2), (x, -pi/3, pi/3))
Numerical answer [src] 
0.133048279484615
0.133048279484615

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

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