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(sin5x)/(9+cos^(2)*5x)

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  • Integral of d{x}:
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  • Identical expressions

  • (sin5x)/(nine +cos^(two)*5x)
  • ( sinus of 5x) divide by (9 plus co sinus of e of to the power of (2) multiply by 5x)
  • ( sinus of 5x) divide by (nine plus co sinus of e of to the power of (two) multiply by 5x)
  • (sin5x)/(9+cos(2)*5x)
  • sin5x/9+cos2*5x
  • (sin5x)/(9+cos^(2)5x)
  • (sin5x)/(9+cos(2)5x)
  • sin5x/9+cos25x
  • sin5x/9+cos^25x
  • (sin5x) divide by (9+cos^(2)*5x)
  • (sin5x)/(9+cos^(2)*5x)dx

  • Similar expressions

  • (sin5x)/(9-cos^(2)*5x)
Solving integrals/ (sin5x)/(9+cos^(2)*5x)

Integral of (sin5x)/(9+cos^(2)*5x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     sin(5*x)     
 |  ------------- dx
 |         2        
 |  9 + cos (5*x)   
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{\sin{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 9}\, dx$$ 
Integral(sin(5*x)/(9 + cos(5*x)^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                           /cos(5*x)\
 |                        atan|--------|
 |    sin(5*x)                \   3    /
 | ------------- dx = C - --------------
 |        2                     15      
 | 9 + cos (5*x)                        
 |                                      
/
$$\int \frac{\sin{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 9}\, dx = C - \frac{\operatorname{atan}{\left(\frac{\cos{\left(5 x \right)}}{3} \right)}}{15}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
      /cos(5)\            
  atan|------|            
      \  3   /   atan(1/3)
- ------------ + ---------
       15            15
$$- \frac{\operatorname{atan}{\left(\frac{\cos{\left(5 \right)}}{3} \right)}}{15} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{15}$$ 
=
= 
      /cos(5)\            
  atan|------|            
      \  3   /   atan(1/3)
- ------------ + ---------
       15            15
$$- \frac{\operatorname{atan}{\left(\frac{\cos{\left(5 \right)}}{3} \right)}}{15} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{15}$$
Упростить
Numerical answer [src] 
0.0151651184346296
0.0151651184346296
The graph
Integral of (sin5x)/(9+cos^(2)*5x) dx

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

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